The document provides information on kinematics equations for particles moving with constant acceleration in a straight line (SUVAT equations). It introduces the variables used in the equations (s, u, v, a, t) and provides examples of using the equations to solve kinematics problems involving displacement, velocity, acceleration, and time. It also presents three additional SUVAT equations and works through examples of solving problems using these equations.
This document discusses kinematics of a particle moving in a straight line. It explains that motion can be represented using speed-time graphs, distance-time graphs, or acceleration-time graphs. The gradient of a speed-time graph represents acceleration, while the area under the graph represents distance traveled. Several examples are provided of constructing and interpreting these graphs to analyze different scenarios of linear motion.
A student is able to:
- Plot and interpret displacement-time and velocity-time graphs
- Determine an object's motion from the shape of the graphs, including whether it is at rest, moving with uniform or non-uniform velocity/acceleration
- Calculate distance, displacement, velocity, and acceleration from displacement-time and velocity-time graphs
- Solve problems involving linear motion using the equations of motion
This document discusses key concepts in physics related to speed, velocity, and acceleration. It defines speed and velocity, explaining that velocity includes both magnitude and direction. It describes how to calculate average speed, acceleration, and deceleration. Graphs of speed versus time and velocity versus time are examined, including how to determine acceleration from gradients and distance from areas. Free fall under gravity and the effects of air resistance on terminal velocity are also summarized.
1. A velocity-time graph represents the variation of an object's velocity over time as it moves in a straight line, with time on the x-axis and velocity on the y-axis.
2. For uniform motion, the graph is a straight line parallel to the x-axis, while for uniform acceleration the graph is a straight line. Non-uniform acceleration can produce graphs of varying shapes.
3. The three laws of motion relate displacement, velocity, acceleration, and time: v = u + at, s = ut + 1/2at2, and 2as = v2 - u2. These equations can be derived and used to analyze motion graphsically.
The document provides information about uniformly accelerated motion along a straight line. It defines key terms like velocity, acceleration, displacement and equations of motion. Several examples are presented to demonstrate the use of equations to solve problems involving uniformly accelerated motion. Examples include calculating acceleration, distance traveled, time taken and velocities given information about an object's motion under constant acceleration along a straight path.
This document discusses key concepts related to motion, including:
- Distance is a scalar quantity that measures the total length of an object's path, while displacement is a vector quantity that measures the change in an object's position.
- Speed is the rate of change of distance and is a scalar, while velocity is the rate of change of displacement and is a vector.
- Graphs can show the relationship between distance, speed, time, and other motion variables. The slope of a distance-time graph represents speed, while the slope of a speed-time graph represents acceleration.
This document discusses distance-time graphs, velocity-time graphs, and standard units for physical properties. Distance-time graphs show steep lines for fast speeds, shallow lines for slow speeds, and flat lines for zero speed. Velocity is calculated from the gradient of a distance-time graph. Velocity-time graphs show increasing, decreasing, or constant speed. The area under a velocity-time graph equals the distance travelled. Common units for physical properties like distance, time, speed, and mass are also listed.
This document discusses kinematics of a particle moving in a straight line. It explains that motion can be represented using speed-time graphs, distance-time graphs, or acceleration-time graphs. The gradient of a speed-time graph represents acceleration, while the area under the graph represents distance traveled. Several examples are provided of constructing and interpreting these graphs to analyze different scenarios of linear motion.
A student is able to:
- Plot and interpret displacement-time and velocity-time graphs
- Determine an object's motion from the shape of the graphs, including whether it is at rest, moving with uniform or non-uniform velocity/acceleration
- Calculate distance, displacement, velocity, and acceleration from displacement-time and velocity-time graphs
- Solve problems involving linear motion using the equations of motion
This document discusses key concepts in physics related to speed, velocity, and acceleration. It defines speed and velocity, explaining that velocity includes both magnitude and direction. It describes how to calculate average speed, acceleration, and deceleration. Graphs of speed versus time and velocity versus time are examined, including how to determine acceleration from gradients and distance from areas. Free fall under gravity and the effects of air resistance on terminal velocity are also summarized.
1. A velocity-time graph represents the variation of an object's velocity over time as it moves in a straight line, with time on the x-axis and velocity on the y-axis.
2. For uniform motion, the graph is a straight line parallel to the x-axis, while for uniform acceleration the graph is a straight line. Non-uniform acceleration can produce graphs of varying shapes.
3. The three laws of motion relate displacement, velocity, acceleration, and time: v = u + at, s = ut + 1/2at2, and 2as = v2 - u2. These equations can be derived and used to analyze motion graphsically.
The document provides information about uniformly accelerated motion along a straight line. It defines key terms like velocity, acceleration, displacement and equations of motion. Several examples are presented to demonstrate the use of equations to solve problems involving uniformly accelerated motion. Examples include calculating acceleration, distance traveled, time taken and velocities given information about an object's motion under constant acceleration along a straight path.
This document discusses key concepts related to motion, including:
- Distance is a scalar quantity that measures the total length of an object's path, while displacement is a vector quantity that measures the change in an object's position.
- Speed is the rate of change of distance and is a scalar, while velocity is the rate of change of displacement and is a vector.
- Graphs can show the relationship between distance, speed, time, and other motion variables. The slope of a distance-time graph represents speed, while the slope of a speed-time graph represents acceleration.
This document discusses distance-time graphs, velocity-time graphs, and standard units for physical properties. Distance-time graphs show steep lines for fast speeds, shallow lines for slow speeds, and flat lines for zero speed. Velocity is calculated from the gradient of a distance-time graph. Velocity-time graphs show increasing, decreasing, or constant speed. The area under a velocity-time graph equals the distance travelled. Common units for physical properties like distance, time, speed, and mass are also listed.
This document provides an overview of graphing motion in one dimension. It discusses position versus time graphs, velocity versus time graphs, and acceleration versus time graphs. Key points include:
- The slope of a position-time graph represents velocity, and the slope of a velocity-time graph represents acceleration.
- Straight lines on position-time graphs indicate uniform motion with constant velocity.
- The area under a velocity-time graph represents displacement.
- Kinematic equations allow calculations of variables like position, velocity, and acceleration given information about an object's motion under constant acceleration.
The document discusses motion, including:
1. Defining displacement and distance travelled.
2. Calculating speed using the equation speed = distance/time.
3. Distinguishing between speed and velocity, with velocity having both magnitude and direction.
This document explains how to interpret distance-time graphs. It discusses that distance is plotted on the y-axis and time on the x-axis. A horizontal line indicates no movement, a straight upward line indicates constant speed, and a curved line shows changing speed. Faster lines have steeper slopes, indicating higher speed. The direction of the line shows if an object is moving away from or toward the starting point.
1. The document discusses distance vs time graphs and how to interpret them to understand an object's motion.
2. A horizontal line on the graph represents constant speed, a straight uphill line represents accelerating speed, and a downhill line represents decelerating speed.
3. The slope of the distance vs time graph directly corresponds to the object's speed, with steeper lines representing faster speeds.
This document discusses free-fall motion and describes an experiment to measure the acceleration due to gravity using a photogate and falling object. The experiment involves dropping an object through a photogate multiple times to collect displacement and time data. Students will then analyze the velocity-time graph to determine the acceleration for each trial and calculate the percent error compared to the accepted value of 9.8 m/s^2. The goal is to perform analysis of free-fall motion and enable students to solve problems involving falling objects.
Ppt on equations of motion by graphival method made by mudit guptaMUDIT GUPTA
This document presents the three equations of motion: 1) acceleration equals change in velocity over time, 2) distance equals initial velocity times time plus half acceleration times time squared, and 3) change in velocity squared equals two times acceleration times change in distance. Graphs are used to derive the equations. A video demonstrates all three equations of motion and the document concludes by recapping the three equations learned through a graphical approach.
The document summarizes key concepts in kinematics including displacement, velocity, acceleration, and motion under constant acceleration. It defines displacement as the difference between an object's initial and final positions, and average velocity as the displacement divided by the time elapsed. Acceleration is defined as the rate of change of velocity with respect to time. Examples are provided to demonstrate calculations of displacement, velocity, acceleration, and motion under gravity. Key equations of motion are also summarized.
This chapter discusses kinematics of linear motion, including:
1) It defines kinematics as the study of motion without considering forces, and describes linear and projectile motion.
2) It introduces key concepts such as displacement, speed, velocity, acceleration and their relationships. Equations for these quantities under constant and uniformly accelerated motion are provided.
3) It describes motion under constant acceleration due to gravity, known as freely falling bodies, and provides the relevant equations.
The document summarizes key concepts from Chapter 2 of a Physics textbook on kinematics of linear motion. It discusses the following in 3 sentences:
Linear motion can be one-dimensional or two-dimensional projectile motion. Equations of motion include relationships between displacement, velocity, acceleration, and time. Uniformly accelerated motion follows equations that relate the initial and final velocity, acceleration, and time to determine displacement and distance traveled.
This document provides information about modeling motion mathematically through graphs of position, velocity, and acceleration over time. It begins by explaining how to interpret and draw position vs. time graphs to determine an object's velocity and motion. It then discusses velocity vs. time graphs and how to determine acceleration from the slope. Finally, it covers acceleration vs. time graphs and free fall due to gravity. The key concepts covered are how to analyze motion using graphs of these variables and the equations that relate position, velocity, acceleration, and time for constant or changing motion.
1) The document discusses 1D kinematics graphs of position, velocity, and acceleration over time.
2) The slope of a position vs. time graph gives velocity, while the slope of a velocity vs. time graph gives acceleration.
3) Taking the derivative of a position, velocity, or acceleration function provides the next variable (velocity, acceleration, or change in acceleration), just as taking the integral of acceleration or velocity functions provides position or change in velocity.
This document provides information about distance-time graphs and how to interpret them. It explains that a straight line on a distance-time graph indicates constant speed, with a steeper line representing faster speed. A horizontal line represents a stationary object. A curved line shows an object that is accelerating or decelerating. Examples of graphs are provided and questions are asked about calculating speeds from the graphs. Readers are also instructed to draw their own distance-time graphs.
This PPT covers relative motion between particles in a very systematic and lucid manner. I hope this PPT will be helpful for instructor's as well as students.
The document discusses kinematics concepts related to curvilinear motion and relative motion analysis. It contains the following key points in 3 sentences:
1) It provides an example problem involving determining the velocity and acceleration of a ball moving in a helical path due to the rotational motion of a power screw.
2) It describes how to analyze relative motion problems by attaching a translating reference frame to a moving object and determining the motion relative to that frame, as well as how to determine absolute motion from relative motion.
3) It discusses concepts like inertial reference frames, constrained motion problems involving connected particles with one or two degrees of freedom, and how to set up and solve examples involving these kinematics topics.
The document discusses equations of motion using velocity-time graphs, including the relationships between displacement, average velocity, and the area under the graph. It provides examples of calculating time for one object to catch up to another using the kinematic equations and information about their initial velocities and accelerations. Practice problems are presented at the end to further illustrate applying the kinematic equations.
1) The document provides information about motion, including definitions of rates, speed, velocity, acceleration, and how to graphically represent these concepts using distance vs time and velocity vs time graphs.
2) Key concepts covered include the difference between speed and velocity, how to calculate average speed and velocity, and the relationship between displacement, velocity, and acceleration.
3) Examples are provided for calculating speed, velocity, acceleration and distance traveled given rates of change over time for various motion scenarios.
The document discusses key concepts related to motion including rest, acceleration, uniform and non-uniform acceleration, circular motion, and graphical representations of motion. It defines rest as no change in position over time, and motion as a change in position over time. Acceleration is defined as the rate of change of velocity. Uniform circular motion occurs when an object travels at constant speed in a circular path, requiring a constant centripetal acceleration directed toward the center. Distance-time and velocity-time graphs can represent motion, with straight lines indicating uniform speed or acceleration.
1) The document discusses position-time graphs and velocity-time graphs, defining uniform motion as having constant velocity in both magnitude and direction.
2) It provides examples of how to determine average and instantaneous velocity from position-time graphs by calculating slopes of lines on the graphs.
3) Instructions are given on how to draw a velocity-time graph based on information from a position-time graph by calculating the slope of each part of the position-time graph to determine velocity.
Distance is the total path traveled and does not include direction, while displacement includes both distance and direction from the starting point to the end point. Speed is the distance traveled per unit of time and does not include direction, while velocity includes both speed and direction. Acceleration is the rate of change of velocity - either in magnitude or direction. It can be calculated using the equation: Acceleration = Change in Velocity / Time.
This document discusses acceleration, including the equation for acceleration and how to determine the shape of an a-t graph from a v-t graph. It provides an example of calculating velocity after times t=1s and t=5s given an initial velocity and acceleration. The document also discusses how to draw displacement-time, velocity-time, and acceleration-time graphs for problems involving constant acceleration. Practice problems are provided.
This document provides an introduction to dynamics and forces acting on particles moving in a straight line. It introduces Newton's second law of motion, which states that force is equal to mass times acceleration (F=ma). It defines key concepts like weight, normal reaction force, friction, tension, and thrust. Examples are provided on using F=ma to calculate acceleration given force and mass, or force given mass and acceleration. The document also discusses resolving forces into perpendicular components and using this to solve problems involving multiple forces acting on an object.
Resistivity and resistance are affected by several factors. The resistivity of a material determines how well it conducts electricity. Resistance increases as resistivity, length, or decreases in area increase. Factors like temperature, material properties, and geometry impact resistance and resistivity. Thermistors have resistance that changes with temperature, allowing them to act as temperature sensors when calibrated in a circuit. Superconductors have zero resistance below a critical temperature threshold, enabling applications like power lines and electromagnets.
This document provides an overview of graphing motion in one dimension. It discusses position versus time graphs, velocity versus time graphs, and acceleration versus time graphs. Key points include:
- The slope of a position-time graph represents velocity, and the slope of a velocity-time graph represents acceleration.
- Straight lines on position-time graphs indicate uniform motion with constant velocity.
- The area under a velocity-time graph represents displacement.
- Kinematic equations allow calculations of variables like position, velocity, and acceleration given information about an object's motion under constant acceleration.
The document discusses motion, including:
1. Defining displacement and distance travelled.
2. Calculating speed using the equation speed = distance/time.
3. Distinguishing between speed and velocity, with velocity having both magnitude and direction.
This document explains how to interpret distance-time graphs. It discusses that distance is plotted on the y-axis and time on the x-axis. A horizontal line indicates no movement, a straight upward line indicates constant speed, and a curved line shows changing speed. Faster lines have steeper slopes, indicating higher speed. The direction of the line shows if an object is moving away from or toward the starting point.
1. The document discusses distance vs time graphs and how to interpret them to understand an object's motion.
2. A horizontal line on the graph represents constant speed, a straight uphill line represents accelerating speed, and a downhill line represents decelerating speed.
3. The slope of the distance vs time graph directly corresponds to the object's speed, with steeper lines representing faster speeds.
This document discusses free-fall motion and describes an experiment to measure the acceleration due to gravity using a photogate and falling object. The experiment involves dropping an object through a photogate multiple times to collect displacement and time data. Students will then analyze the velocity-time graph to determine the acceleration for each trial and calculate the percent error compared to the accepted value of 9.8 m/s^2. The goal is to perform analysis of free-fall motion and enable students to solve problems involving falling objects.
Ppt on equations of motion by graphival method made by mudit guptaMUDIT GUPTA
This document presents the three equations of motion: 1) acceleration equals change in velocity over time, 2) distance equals initial velocity times time plus half acceleration times time squared, and 3) change in velocity squared equals two times acceleration times change in distance. Graphs are used to derive the equations. A video demonstrates all three equations of motion and the document concludes by recapping the three equations learned through a graphical approach.
The document summarizes key concepts in kinematics including displacement, velocity, acceleration, and motion under constant acceleration. It defines displacement as the difference between an object's initial and final positions, and average velocity as the displacement divided by the time elapsed. Acceleration is defined as the rate of change of velocity with respect to time. Examples are provided to demonstrate calculations of displacement, velocity, acceleration, and motion under gravity. Key equations of motion are also summarized.
This chapter discusses kinematics of linear motion, including:
1) It defines kinematics as the study of motion without considering forces, and describes linear and projectile motion.
2) It introduces key concepts such as displacement, speed, velocity, acceleration and their relationships. Equations for these quantities under constant and uniformly accelerated motion are provided.
3) It describes motion under constant acceleration due to gravity, known as freely falling bodies, and provides the relevant equations.
The document summarizes key concepts from Chapter 2 of a Physics textbook on kinematics of linear motion. It discusses the following in 3 sentences:
Linear motion can be one-dimensional or two-dimensional projectile motion. Equations of motion include relationships between displacement, velocity, acceleration, and time. Uniformly accelerated motion follows equations that relate the initial and final velocity, acceleration, and time to determine displacement and distance traveled.
This document provides information about modeling motion mathematically through graphs of position, velocity, and acceleration over time. It begins by explaining how to interpret and draw position vs. time graphs to determine an object's velocity and motion. It then discusses velocity vs. time graphs and how to determine acceleration from the slope. Finally, it covers acceleration vs. time graphs and free fall due to gravity. The key concepts covered are how to analyze motion using graphs of these variables and the equations that relate position, velocity, acceleration, and time for constant or changing motion.
1) The document discusses 1D kinematics graphs of position, velocity, and acceleration over time.
2) The slope of a position vs. time graph gives velocity, while the slope of a velocity vs. time graph gives acceleration.
3) Taking the derivative of a position, velocity, or acceleration function provides the next variable (velocity, acceleration, or change in acceleration), just as taking the integral of acceleration or velocity functions provides position or change in velocity.
This document provides information about distance-time graphs and how to interpret them. It explains that a straight line on a distance-time graph indicates constant speed, with a steeper line representing faster speed. A horizontal line represents a stationary object. A curved line shows an object that is accelerating or decelerating. Examples of graphs are provided and questions are asked about calculating speeds from the graphs. Readers are also instructed to draw their own distance-time graphs.
This PPT covers relative motion between particles in a very systematic and lucid manner. I hope this PPT will be helpful for instructor's as well as students.
The document discusses kinematics concepts related to curvilinear motion and relative motion analysis. It contains the following key points in 3 sentences:
1) It provides an example problem involving determining the velocity and acceleration of a ball moving in a helical path due to the rotational motion of a power screw.
2) It describes how to analyze relative motion problems by attaching a translating reference frame to a moving object and determining the motion relative to that frame, as well as how to determine absolute motion from relative motion.
3) It discusses concepts like inertial reference frames, constrained motion problems involving connected particles with one or two degrees of freedom, and how to set up and solve examples involving these kinematics topics.
The document discusses equations of motion using velocity-time graphs, including the relationships between displacement, average velocity, and the area under the graph. It provides examples of calculating time for one object to catch up to another using the kinematic equations and information about their initial velocities and accelerations. Practice problems are presented at the end to further illustrate applying the kinematic equations.
1) The document provides information about motion, including definitions of rates, speed, velocity, acceleration, and how to graphically represent these concepts using distance vs time and velocity vs time graphs.
2) Key concepts covered include the difference between speed and velocity, how to calculate average speed and velocity, and the relationship between displacement, velocity, and acceleration.
3) Examples are provided for calculating speed, velocity, acceleration and distance traveled given rates of change over time for various motion scenarios.
The document discusses key concepts related to motion including rest, acceleration, uniform and non-uniform acceleration, circular motion, and graphical representations of motion. It defines rest as no change in position over time, and motion as a change in position over time. Acceleration is defined as the rate of change of velocity. Uniform circular motion occurs when an object travels at constant speed in a circular path, requiring a constant centripetal acceleration directed toward the center. Distance-time and velocity-time graphs can represent motion, with straight lines indicating uniform speed or acceleration.
1) The document discusses position-time graphs and velocity-time graphs, defining uniform motion as having constant velocity in both magnitude and direction.
2) It provides examples of how to determine average and instantaneous velocity from position-time graphs by calculating slopes of lines on the graphs.
3) Instructions are given on how to draw a velocity-time graph based on information from a position-time graph by calculating the slope of each part of the position-time graph to determine velocity.
Distance is the total path traveled and does not include direction, while displacement includes both distance and direction from the starting point to the end point. Speed is the distance traveled per unit of time and does not include direction, while velocity includes both speed and direction. Acceleration is the rate of change of velocity - either in magnitude or direction. It can be calculated using the equation: Acceleration = Change in Velocity / Time.
This document discusses acceleration, including the equation for acceleration and how to determine the shape of an a-t graph from a v-t graph. It provides an example of calculating velocity after times t=1s and t=5s given an initial velocity and acceleration. The document also discusses how to draw displacement-time, velocity-time, and acceleration-time graphs for problems involving constant acceleration. Practice problems are provided.
This document provides an introduction to dynamics and forces acting on particles moving in a straight line. It introduces Newton's second law of motion, which states that force is equal to mass times acceleration (F=ma). It defines key concepts like weight, normal reaction force, friction, tension, and thrust. Examples are provided on using F=ma to calculate acceleration given force and mass, or force given mass and acceleration. The document also discusses resolving forces into perpendicular components and using this to solve problems involving multiple forces acting on an object.
Resistivity and resistance are affected by several factors. The resistivity of a material determines how well it conducts electricity. Resistance increases as resistivity, length, or decreases in area increase. Factors like temperature, material properties, and geometry impact resistance and resistivity. Thermistors have resistance that changes with temperature, allowing them to act as temperature sensors when calibrated in a circuit. Superconductors have zero resistance below a critical temperature threshold, enabling applications like power lines and electromagnets.
This document contains an exam paper for Core Mathematics C4. It includes 5 questions testing calculus skills. The paper provides instructions for candidates, advising them to show working, write answers in the spaces provided, and use an appropriate degree of accuracy when using a calculator. It also lists the materials candidates may use and information about the duration, marks and structure of the exam.
The document provides information about Arnold Schoenberg's piece "Peripetie" including definitions of musical terms used in the piece such as hexachord, diminution, and glissando. It gives one example of Schoenberg's use of canon and explains that atonal music has no set key or tonality. The document also identifies that symbols "H" and "N" represent the most and second most important melodies. It cites five features showing the piece was composed in the 20th century including its atonal angular style, use of extended techniques, focus on timbre, and lack of clear form.
Este documento contiene 10 problemas de sistemas de ecuaciones que deben resolverse mediante sustitución. Se proporcionan las ecuaciones para cada sistema, así como las respuestas una vez resueltos.
The document discusses the benefits of meditation for reducing stress and anxiety. Regular meditation practice can help calm the mind and body by lowering heart rate and blood pressure. Studies have shown that meditating for just 10-20 minutes per day can have significant positive impacts on both mental and physical health.
This document provides instructions and information for a mathematics exam. It includes:
1) Details about the exam such as the date, time allotted, and materials allowed.
2) Instructions for candidates on how to identify their work and provide their information.
3) Information for candidates about the structure of the exam including the total number and types of questions, and the total marks available.
4) Advice to candidates about showing their working and obtaining full credit.
This document provides information about an exam for the Edexcel GCE Core Mathematics C3 Bronze Level B1 qualification. It lists the paper reference, time allowed, materials required and permitted calculators. It provides instructions for candidates on writing details on the front page and information about the structure of the paper. It also lists the 9 questions that make up the exam, covering topics like functions, graphs, derivatives, iterations and logarithms. The final section suggests grade boundaries for the exam.
This document appears to be an exam paper for a mechanics course. It contains 6 multiple part questions testing concepts in mechanics such as forces, kinematics, and dynamics. The questions provide contextual word problems and diagrams requiring students to set up and solve equations to find requested values. The exam paper provides space for work and answers and includes instructions for candidates on providing responses. It is signed and includes information for examiners.
This document provides information about a Core Mathematics C3 exam taken by Edexcel students. It includes instructions for students taking the exam, information about materials allowed and provided, and 8 questions testing various calculus, geometry, and trigonometry concepts. The exam is 1 hour and 30 minutes long and contains a total of 75 marks across the 8 questions. Students are advised to show their working clearly and label answers to parts of questions.
This document contains an exam paper for a Core Mathematics C3 Advanced exam. It provides instructions for candidates on how to fill out their details, contains 9 questions to answer, and specifies the time allotted and materials allowed. Candidates are to show their working and answers must be written in the spaces provided after each question.
The document provides revision notes on various mathematics topics including:
1) Binomial expansions, partial fractions, trigonometry formulas, and techniques for integration like volumes of revolution.
2) Parametric equations, vectors, vector equations, planes, and differential equations.
3) Details are given for solving problems involving these topics, such as using compound angle formulas, rewriting algebraic fractions as partial fractions, and separating variables to solve first-order differential equations.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help boost feelings of calmness, happiness and focus.
This document appears to be an exam paper for a mathematics course. It contains instructions for candidates taking the exam, information about the structure and format of the exam, the exam questions themselves, and spaces for candidates to write their answers. The exam consists of 9 multiple choice and short answer questions testing a range of mathematics concepts and skills, including binomial expansion, solving equations, factorizing polynomials, calculating areas, and using integration rules. Candidates are instructed to show their working, write answers in the spaces provided, and include relevant working and steps to receive full marks. The first 3 questions are presented for summary.
This document covers several topics in calculus including differentiation, implicit differentiation, transformations, trigonometry, vectors, and integration.
The document discusses electricity and resistance. It defines resistance as the ratio of voltage to current and explains that resistance depends on a material's resistivity, length, and cross-sectional area. It introduces Georg Ohm and Ohm's Law, which states that voltage and current are directly proportional. Resistors are circuit elements that produce voltage proportional to current according to Ohm's Law. Conductors contain movable electric charges like electrons that allow current to flow. Insulators contain fewer movable charges and resist current. The document contrasts alternating and direct current, noting that DC involves a constant unidirectional flow of charge.
This document provides summaries and examples of various mathematical topics including:
- Arithmetic properties such as associative, commutative, and distributive properties
- Exponent properties and properties of inequalities
- Steps for solving quadratic equations
- Algebra properties and calculus topics such as derivatives, limits, and integrals
- Geometric shapes and solids and their volume formulas
- Trigonometric functions, inverse trig functions, trig identities, and law of sines, cosines, and tangents.
This document discusses vectors and vector addition in two and three dimensions. It provides examples of displacement vectors, distance traveled, and the relationship between the two. It also contains problems calculating vector components, magnitudes, and directions in various scenarios involving particle motion along paths and circles. Solutions are provided for each multi-part problem.
The document provides information about analyzing motion using ticker tape diagrams. It discusses how a ticker tape timer works by making dots at regular intervals. The distance between dots represents the position change of an object during that interval. A large distance between dots indicates high speed, while a small distance indicates low speed. Ticker tape diagrams can reveal if an object is moving at constant velocity or with changing velocity (accelerating). Gradient analysis of displacement-time and velocity-time graphs can determine velocity and acceleration respectively. Several examples are given and questions provided to illustrate using ticker tape diagrams to analyze motion.
This document covers the topic of kinematics, which is the study of motion without regard to its causes. It discusses various kinematic concepts including linear and angular displacement, velocity, acceleration, and their relationships. Formulas are derived for uniformly accelerated motion based on definitions of terms and velocity-time graphs. Examples problems apply the concepts and formulas to analyze the linear and rotational motion of objects undergoing changes in velocity such as cars accelerating and decelerating. The document also addresses projectile and free-fall motion under the acceleration of gravity.
The document defines key terms related to linear motion such as scalar and vector quantities, linear and non-uniform motion, distance, displacement, speed, velocity, acceleration, and deceleration. It provides formulas for calculating these quantities and illustrates them with examples. It also describes how to apply the concepts of linear motion to solve related problems using the appropriate formulas and how to interpret velocity-time graphs to determine velocity, acceleration, and displacement.
1. The document discusses various concepts related to one-dimensional motion including position, distance, displacement, speed, velocity, and acceleration.
2. It defines key terms like displacement as the change in position of an object, velocity as a vector quantity that includes both speed and direction, and acceleration as the rate of change of velocity with respect to time.
3. Examples and equations are provided to calculate quantities like average speed, average velocity, and instantaneous velocity from distance-time graphs or data tables.
GRAPHICAL REPRESENTATION OF MOTION💖.pptxssusere853b3
Graphical representations like distance-time graphs and velocity-time graphs can be used to describe motion. Distance-time graphs show the dependence of distance on time, with distance on the y-axis and time on the x-axis. The slope of a distance-time graph gives the object's speed. Velocity-time graphs show the dependence of velocity on time, with velocity on the y-axis and time on the x-axis. The area under a velocity-time graph gives the object's displacement. These graphs can indicate whether motion is uniform or non-uniform and can be used to calculate values like speed, velocity, distance, and acceleration.
This document discusses linear motion and related concepts such as distance, displacement, speed, velocity, and acceleration.
Linear motion is motion in a straight line, while examples of non-linear motion include circular motion such as a roller coaster ride. Distance is the total length travelled regardless of direction, whereas displacement considers both length and direction between two points.
Speed is a scalar quantity that measures the rate of change of distance with time. Velocity is a vector quantity that considers both the rate of change of displacement over time as well as direction. Acceleration is the rate of change of velocity, and can be positive (acceleration) or negative (deceleration).
Formulas are provided to calculate quantities like average speed,
The document describes the motion of a lift cage over time. It moves upwards with constant acceleration from rest until reaching a maximum speed, then moves at a constant speed until slowing down with constant negative acceleration to a stop. A spring hanging from the ceiling stretches during acceleration and shrinks during deceleration to provide the forces needed for the cage's changing acceleration according to Newton's laws. The document provides graphs of position, speed, and acceleration over time and explains the kinematics using these variables.
This document provides an overview of A-Level Physics content on kinematics and SUVAT equations. It aims to teach students how to use equations for uniformly accelerated motion in one dimension, as well as how to separate vertical and horizontal motion of projectiles. The lesson covers definitions of kinematics, derivation of basic SUVAT equations, worked examples, and practice questions to solidify understanding of calculating velocity, displacement, time and acceleration using the SUVAT method.
1. The document describes motion and kinematic equations derived from velocity-time and distance-time graphs. It defines concepts like displacement, distance, speed, velocity, uniform and non-uniform motion, and acceleration.
2. Equations of motion like v=u+at, s=ut+1/2at^2, and 2as=v^2-u^2 are derived graphically from velocity-time graphs for bodies undergoing uniform acceleration.
3. Circular motion is defined as motion along a circular path. Uniform circular motion occurs when an object moves at a constant speed but continuously changes direction, resulting in acceleration.
The document defines key concepts related to linear motion, including:
- Scalar and vector quantities, with scalar having only magnitude and vector having both magnitude and direction.
- Linear motion as motion in a straight line, described by distance, displacement, speed, velocity, and their relationships.
- Uniform motion as maintaining a constant speed in a straight line, versus non-uniform motion changing speed or direction.
- Formulas for calculating velocity, acceleration, and displacement from information about initial/final velocities and time.
- Examples of using these formulas to solve problems involving distance, speed, velocity, and acceleration for objects in linear motion.
- Illustrations of velocity-time graphs showing changes in velocity over time for
This document describes motion and kinematics concepts for class 9 science. It defines key terms like displacement, distance, speed, velocity, uniform and non-uniform motion. It discusses representing motion graphically using distance-time and velocity-time graphs. The three equations of motion relating displacement, velocity, acceleration and time are derived from these graphs. Circular motion is also introduced.
1. The document describes motion and key concepts related to motion including: distance, displacement, speed, velocity, uniform and non-uniform motion, acceleration, and equations of motion.
2. Graphs are used to represent motion including distance-time graphs and velocity-time graphs which can show uniform and non-uniform motion.
3. Equations of motion relating velocity, displacement, time, initial velocity, final velocity, and acceleration are derived using the area under velocity-time graphs.
4. Circular motion is described as motion along a circular path which is an accelerated motion due to continuous change in direction.
1. Motion is defined as a change in position of an object over time. Distance moved is the total path travelled, while displacement is the shortest distance between the starting and ending points.
2. Uniform motion means equal distances are travelled in equal times, while non-uniform motion means unequal distances are travelled in equal times. Velocity is the rate of change of an object's displacement and includes both speed and direction.
3. Acceleration is the rate of change of velocity with time. Uniform acceleration means equal changes in velocity over equal times, while non-uniform acceleration means unequal changes in velocity over equal times.
1. Motion is defined as a change in position of an object over time. Distance moved is the total path travelled, while displacement is the shortest distance between the starting and ending points.
2. Uniform motion means equal distances are travelled in equal times, while non-uniform motion means unequal distances are travelled in equal times. Velocity is the rate of change of an object's displacement and includes both speed and direction.
3. Acceleration is the rate of change of velocity with time. Uniform acceleration means equal changes in velocity over equal times, while non-uniform acceleration means unequal changes in velocity over equal times.
1. Motion is defined as a change in position of an object over time. Distance moved is the total path travelled, while displacement is the shortest distance between the starting and ending points.
2. Uniform motion means equal distances are travelled in equal times, while non-uniform motion means unequal distances are travelled in equal times. Velocity is the rate of change of an object's displacement and includes both speed and direction.
3. Acceleration is the rate of change of velocity with time. Uniform acceleration means equal changes in velocity over equal times, while non-uniform acceleration means unequal changes in velocity over equal times.
1. The document describes motion and kinematic concepts like displacement, distance, speed, velocity, uniform and non-uniform motion, acceleration, and equations of motion.
2. Graphs of distance-time and velocity-time are used to represent motion and determine quantities like speed and acceleration from the slope of the graphs.
3. Circular motion is also described, where uniform circular motion involves constant speed but accelerated motion due to continuous change in direction.
This document describes motion and kinematics concepts for class 9 students. It defines key terms like distance, displacement, speed, velocity, uniform and non-uniform motion, acceleration, and equations of motion. Distance is the total path travelled while displacement is the shortest path between initial and final positions. Speed is defined as distance/time while velocity includes both magnitude and direction of motion. Uniform motion has equal distances travelled in equal time intervals while non-uniform motion does not. Acceleration is the rate of change of velocity with time. Motion can be represented graphically using distance-time and velocity-time graphs. Equations of motion relate the relationships between displacement, velocity, acceleration, and time. Circular motion describes motion along a circular
1. The document describes various concepts related to motion including speed, velocity, acceleration, and how to represent motion graphically. It defines key terms like reference point, displacement, and scalar and vector quantities.
2. Examples are provided for calculating speed, acceleration, and time it takes for an object to travel a distance or come to a stop.
3. Motion can be represented on distance-time or speed-time graphs where slope and shape of the line indicate properties of motion like constant speed or changing velocity.
1) Motion can be uniform or non-uniform, depending on whether the body travels equal or unequal distances in equal time intervals. Speed, velocity, and acceleration are defined in terms of distance, displacement, and time.
2) The area under a speed-time graph provides the distance traveled, while the slope of the line in such a graph gives the acceleration. The three equations of motion relate the variables of displacement, velocity, acceleration, and time.
3) Circular motion occurs when a body moves along a circular path, changing direction continuously. Uniform circular motion refers to constant speed around the path.
This document introduces vectors and how they can be used to describe displacements and solve problems involving displacement. It discusses that vectors have both direction and magnitude, and provides examples. Vectors can be added and represented using line segments. The triangle law of addition allows vectors to be added using a triangle. Vectors can also be described using i and j notation, where i and j are unit vectors along the x and y axes, and any two-dimensional vector can be written as ai + bj. Problems can then be solved by adding or subtracting the i and j terms. The magnitude of a vector can be found using Pythagoras' theorem, and the angle between a vector and an axis can be found using trig
- A particle starts from the point with position vector (3i + 7j) m and then moves with constant velocity (2i – j) ms-1. The question asks to find the position vector of the particle 4 seconds later.
- Substituting the values into the displacement equation gives the final position vector as (12i + 3j) m.
- A second particle is given a position vector of (2i + 4j) m at time t = 0 and a position vector of (12i + 16j) m five seconds later. Using the displacement equation gives the velocity of the particle as (2i + 4j) ms-1.
- For a third particle
(1) The document discusses moments, which are turning forces that cause an object to rotate rather than push it linearly. Moments depend on the magnitude of the applied force and its distance from the pivot point.
(2) To calculate the moment of a single force, the formula is Moment = Force x Perpendicular Distance from the pivot. When multiple forces are present, their individual moments are summed.
(3) Systems in equilibrium have their clockwise and counter-clockwise moments equal, allowing one to solve for unknown values like reactions at supports. Diagrams are drawn and moments taken to set up and solve equations of equilibrium.
This chapter focuses on objects in static equilibrium, where the net force and net torque on the object are both zero. Solving static equilibrium problems involves drawing free body diagrams showing all external forces acting on the object, then resolving forces into components and setting the sums of forces in each direction equal to zero. Three examples are given of solving static equilibrium problems involving particles under the influence of multiple forces. The problems are solved by resolving forces into horizontal and vertical or parallel and perpendicular components, setting the component force equations equal to zero, and solving the equations to determine the magnitudes of unknown forces. Key steps include drawing diagrams, resolving forces, setting force sums to zero, and solving the resulting equations.
This document provides an introduction to dynamics and forces acting on particles moving in a straight line. It introduces Newton's second law of motion, F=ma, and defines key concepts like weight, tension, thrust, friction, and normal reaction. It explains how to resolve forces into horizontal and vertical components when multiple forces are acting. Examples show how to set up force diagrams and use Newton's second law to solve for acceleration, distance, and missing forces. Trigonometry is used to resolve forces acting at angles into their x- and y-direction components.
The document discusses increasing and decreasing functions. An increasing function has a positive gradient, while a decreasing function has a negative gradient. Some functions can be increasing over one interval and decreasing over another. You need to be able to determine the intervals where a function is increasing or decreasing by examining its gradient. The document provides examples of finding where a function is decreasing by taking the derivative, setting it equal to 0, and solving for the range of x-values that make the gradient negative. It also discusses using derivatives to find the coordinates of stationary points like maxima and minima, and using the second derivative to determine if a stationary point is a maximum or minimum.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
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This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
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Main Java[All of the Base Concepts}.docxadhitya5119
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This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
2. Introduction
• This chapter you will learn the SUVAT
equations
• These are the foundations of many of
the Mechanics topics
• You will see how to use them to use
many types of problem involving motion
3.
4. Kinematics of a Particle moving in a
Straight Line
You will begin by learning two of the
SUVAT equations
s = Displacement (distance)
u = Starting (initial) velocity
v = Final velocity
a = Acceleration
t = Time
Multiply by t
Replace with the
appropriate letters.
Change in velocity =
final velocity – initial
velocity
Add u
This is the
usual form!
Replace
with the
appropriate
letters
2A
5. Kinematics of a Particle moving in a
Straight Line
You will begin by learning two of the
SUVAT equations
s = Displacement (distance)
u = Starting (initial) velocity
v = Final velocity
a = Acceleration
t = Time
You need to consider using negative numbers in
some cases
Positive direction
2.5ms-1
6ms-1
P
Q
4m
O
3m
If we are measuring displacements from O, and left to right
is the positive direction…
For particle P:
The particle is to the left of
the point O, which is the
negative direction
The particle is moving at
2.5ms-1 in the positive direction
The particle is to
the right of the
point O, which is
the positive
direction
The particle is moving at 6ms-1
in the negative direction
For particle Q:
2A
6. Kinematics of a Particle moving in a
Straight Line
You will begin by learning
two of the SUVAT
equations
s = Displacement (distance)
u = Starting (initial) velocity
v = Final velocity
a = Acceleration
t = Time
A particle is moving in a straight line from A to B with constant
acceleration 3ms-2. Its speed at A is 2ms-1 and it takes 8 seconds to
move from A to B. Find:
a) The speed of the particle at B
b) The distance from A to B
2ms-1
Start with a
diagram
A
B
Write out ‘suvat’ and
fill in what you know
Fill in the
values you
know
For part a) we need
to calculate v, and we
know u, a and t…
Remember to
include units!
You always need to set up the question in this
way. It makes it much easier to figure out what
equation you need to use (there will be more to
learn than just these two!)
2A
7. Kinematics of a Particle moving in a
Straight Line
You will begin by learning
two of the SUVAT
equations
s = Displacement (distance)
u = Starting (initial) velocity
v = Final velocity
a = Acceleration
t = Time
A particle is moving in a straight line from A to B with constant
acceleration 3ms-2. Its speed at A is 2ms-1 and it takes 8 seconds to
move from A to B. Find:
a) The speed of the particle at B – 26ms-1
b) The distance from A to B
2ms-1
A
B
Fill in the
values you
know
For part b) we need
to calculate s, and we
know u, v and t…
Show
calculations
Remember
the units!
2A
8. Kinematics of a Particle moving in a
Straight Line
You will begin by learning
two of the SUVAT
equations
s = Displacement (distance)
u = Starting (initial) velocity
v = Final velocity
a = Acceleration
t = Time
A cyclist is travelling along a straight road. She accelerates at a
constant rate from a speed of 4ms-1 to a speed of 7.5ms-1 in 40
seconds. Find:
a) The distance travelled over this 40 seconds
b) The acceleration over the 40 seconds
4ms-1
7.5ms-1
Draw a diagram
(model the cyclist as
a particle)
Write out ‘suvat’ and
fill in what you know
Sub in the
values you
know
We are calculating
s, and we already
know u, v and t…
Remember
units!
2A
9. Kinematics of a Particle moving in a
Straight Line
You will begin by learning
two of the SUVAT
equations
s = Displacement (distance)
u = Starting (initial) velocity
v = Final velocity
a = Acceleration
t = Time
A cyclist is travelling along a straight road. She accelerates at a
constant rate from a speed of 4ms-1 to a speed of 7.5ms-1 in 40
seconds. Find:
a) The distance travelled over this 40 seconds – 230m
b) The acceleration over the 40 seconds
4ms-1
7.5ms-1
Draw a diagram
(model the cyclist as
a particle)
Write out ‘suvat’ and
fill in what you know
Sub in the
values you
know
For part b, we are
calculating a, and we
already know u, v and
t…
Subtract 4
Divide by
40
2A
10. Kinematics of a Particle moving in a
Straight Line
You will begin by learning
two of the SUVAT
equations
s = Displacement (distance)
u = Starting (initial) velocity
v = Final velocity
a = Acceleration
t = Time
A particle moves in a straight line from a point A to B with constant
deceleration of 1.5ms-2. The speed of the particle at A is 8ms-1 and the
speed of the particle at B is 2ms-1. Find:
a) The time taken for the particle to get from A to B
b) The distance from A to B
8ms-1
2ms-1
Draw a diagram
A
B
Sub in the
values you know
Write out ‘suvat’ and
fill in what you know
As the particle is
decelerating, ‘a’ is
negative
Subtract 8
Divide by -1.5
2A
11. Kinematics of a Particle moving in a
Straight Line
You will begin by learning
two of the SUVAT
equations
s = Displacement (distance)
u = Starting (initial) velocity
v = Final velocity
a = Acceleration
t = Time
A particle moves in a straight line from a point A to B with constant
deceleration of 1.5ms-2. The speed of the particle at A is 8ms-1 and the
speed of the particle at B is 2ms-1. Find:
a) The time taken for the particle to get from A to B – 4 seconds
b) The distance from A to B
8ms-1
2ms-1
Draw a diagram
A
B
Sub in the
values you know
Write out ‘suvat’ and
fill in what you know
As the particle is
decelerating, ‘a’ is
negative
Calculate the
answer!
2A
12. Kinematics of a Particle moving in a
Straight Line
You will begin by learning
two of the SUVAT
equations
s = Displacement (distance)
u = Starting (initial) velocity
v = Final velocity
a = Acceleration
t = Time
After reaching B the particle continues to move along the straight line
with the same deceleration. The particle is at point C, 6 seconds after
passing through A. Find:
a) The velocity of the particle at C
b) The distance from A to C
8ms-1
A
2ms-1
B
?
Update the
diagram
C
Write out
‘suvat’ using
points A and C
Sub in the
values
Work it
out!
As the velocity is negative, this means the
particle has now changed direction and is
heading back towards A! (velocity has a
direction as well as a magnitude!)
The velocity is 1ms-1 in the direction C to A…
2A
13. Kinematics of a Particle moving in a
Straight Line
You will begin by learning
two of the SUVAT
equations
s = Displacement (distance)
u = Starting (initial) velocity
v = Final velocity
a = Acceleration
t = Time
After reaching B the particle continues to move along the straight line
with the same deceleration. The particle is at point C, 6 seconds after
passing through A. Find:
a) The velocity of the particle at C - -1ms-1
b) The distance from A to C
8ms-1
2ms-1
A
B
?
Update the
diagram
C
Write out
‘suvat’ using
points A and C
Sub in the
values
Work it
out!
It is important to note that 21m is the distance from A to C
only…
The particle was further away before it changed
direction, and has in total travelled further than 21m…
2A
14. Kinematics of a Particle moving in a
Straight Line
You will begin by learning
two of the SUVAT
equations
s = Displacement (distance)
u = Starting (initial) velocity
v = Final velocity
a = Acceleration
t = Time
A car moves from traffic lights along a straight road with constant
acceleration. The car starts from rest at the traffic lights and 30
seconds later passes a speed trap where it is travelling at 45 kmh-1. Find:
a) The acceleration of the car
b) The distance between the traffic lights and the speed-trap.
0ms-1
45kmh-1
Draw a diagram
Lights
Trap
Standard units to use are metres and seconds, or kilometres and hours
In this case, the time is in seconds and the speed is in kilometres
per hour
We need to change the speed into metres per second first!
Multiply by 1000 (km to m)
Divide by 3600 (hours to seconds)
2A
15. Kinematics of a Particle moving in a
Straight Line
You will begin by learning
two of the SUVAT
equations
s = Displacement (distance)
u = Starting (initial) velocity
v = Final velocity
a = Acceleration
t = Time
A car moves from traffic lights along a straight road with constant
acceleration. The car starts from rest at the traffic lights and 30
seconds later passes a speed trap where it is travelling at 45 kmh-1. Find:
a) The acceleration of the car
b) The distance between the traffic lights and the speed-trap.
0ms-1
45kmh-1 = 12.5ms-1
Draw a diagram
Lights
Trap
Write out ‘suvat’ and
fill in what you know
Sub in the
values
Divide by
30
You can use
exact answers!
2A
16. Kinematics of a Particle moving in a
Straight Line
You will begin by learning
two of the SUVAT
equations
s = Displacement (distance)
u = Starting (initial) velocity
v = Final velocity
a = Acceleration
t = Time
A car moves from traffic lights along a straight road with constant
acceleration. The car starts from rest at the traffic lights and 30
seconds later passes a speed trap where it is travelling at 45 kmh-1. Find:
a) The acceleration of the car
b) The distance between the traffic lights and the speed-trap.
0ms-1
45kmh-1 = 12.5ms-1
Draw a diagram
Lights
Trap
Write out ‘suvat’ and
fill in what you know
Sub in
values
Work it
out!
2A
17.
18. Kinematics of a Particle moving in a
Straight Line
You can also use 3 more formulae linking
different combination of ‘SUVAT’, for a
particle moving in a straight line with
constant acceleration
Subtract u
Divide by a
Replace t with the
expression above
Multiply numerators and
denominators
Multiply by 2a
Add u2
This is the way it is
usually written!
2B
19. Kinematics of a Particle moving in a
Straight Line
You can also use 3 more formulae linking
different combination of ‘SUVAT’, for a
particle moving in a straight line with
constant acceleration
Replace ‘v’ with ‘u + at’
Group terms on the
numerator
Divide the numerator
by 2
Multiply out the
bracket
2B
20. Kinematics of a Particle moving in a
Straight Line
You can also use 3 more formulae linking
different combination of ‘SUVAT’, for a
particle moving in a straight line with
constant acceleration
Subtract ‘at’
Replace ‘u’ with ‘v - at’
from above’
Multiply out the
bracket
Group up the at2
terms
2B
21. Kinematics of a Particle moving in a
Straight Line
You can also use 3 more formulae
linking different combination of
‘SUVAT’, for a particle moving in
a straight line with constant
acceleration
A particle is moving in a straight line from A to B with constant
acceleration 5ms-2. The velocity of the particle at A is 3ms-1 in the
direction AB. The velocity at B is 18ms-1 in the same direction. Find the
distance from A to B.
3ms-1
18ms-1
Draw a diagram
A
B
Write out ‘suvat’
with the
information given
Replace v, u and a
We are
calculating
s, using v, u and a
Work out terms
Subtract 9
Divide by 10
2B
22. Kinematics of a Particle moving in a
Straight Line
You can also use 3 more formulae
linking different combination of
‘SUVAT’, for a particle moving in
a straight line with constant
acceleration
A car is travelling along a straight horizontal road with a constant
acceleration of 0.75ms-2. The car is travelling at 8ms-1 as it passes a
pillar box. 12 seconds later the car passes a lamp post. Find:
a) The distance between the pillar box and the lamp post
b) The speed with which the car passes the lamp post
8ms-1
Pillar
Box
Draw a diagram
Write out ‘suvat’
with the
information given
Lamp
Post
We are
calculating
s, using u, a and t
Replace u, a
and t
Calculate
2B
23. Kinematics of a Particle moving in a
Straight Line
You can also use 3 more formulae
linking different combination of
‘SUVAT’, for a particle moving in
a straight line with constant
acceleration
A car is travelling along a straight horizontal road with a constant
acceleration of 0.75ms-2. The car is travelling at 8ms-1 as it passes a
pillar box. 12 seconds later the car passes a lamp post. Find:
a) The distance between the pillar box and the lamp post – 150m
b) The speed with which the car passes the lamp post
8ms-1
Pillar
Box
Draw a diagram
Lamp
Post
Write out ‘suvat’
with the
information given
We are
calculating
v, using u, a and t
Replace u, a
and t
Calculate
Often you can use an answer you have calculated later
on in the same question. However, you must take care
to use exact values and not rounded answers!
2B
24. Kinematics of a Particle moving in a
Straight Line
You can also use 3 more formulae
linking different combination of
‘SUVAT’, for a particle moving in
a straight line with constant
acceleration
A particle is moving in a straight horizontal line with constant
deceleration 4ms-2. At time t = 0 the particle passes through a point O
with speed 13ms-1, travelling to a point A where OA = 20m. Find:
a) The times when the particle passes through A
b) The total time the particle is beyond A
c) The time taken for the particle to return to O
Draw a diagram
13ms-1
O
A
Replace s, u
and a
Write out ‘suvat’
with the
information given
We are
calculating
t, using s, u and a
Simplify terms
We have 2 answers. As the
acceleration is negative, the
particle passes through A, then
changes direction and passes
through it again!
Rearrange and set equal to 0
Factorise (or use the quadratic formula…)
2B
25. Kinematics of a Particle moving in a
Straight Line
You can also use 3 more formulae
linking different combination of
‘SUVAT’, for a particle moving in
a straight line with constant
acceleration
A particle is moving in a straight horizontal line with constant
deceleration 4ms-2. At time t = 0 the particle passes through a point O
with speed 13ms-1, travelling to a point A where OA = 20m. Find:
a) The times when the particle passes through A – 2.5 and 4 seconds
b) The total time the particle is beyond A
c) The time taken for the particle to return to O
Draw a diagram
13ms-1
O
A
The particle passes through A at 2.5
seconds and 4 seconds, so it was
beyond A for 1.5 seconds…
Write out ‘suvat’
with the
information given
We are
calculating
t, using s, u and a
2B
26. Kinematics of a Particle moving in a
Straight Line
You can also use 3 more formulae
linking different combination of
‘SUVAT’, for a particle moving in
a straight line with constant
acceleration
A particle is moving in a straight horizontal line with constant
deceleration 4ms-2. At time t = 0 the particle passes through a point O
with speed 13ms-1, travelling to a point A where OA = 20m. Find:
a) The times when the particle passes through A – 2.5 and 4 seconds
b) The total time the particle is beyond A – 1.5 seconds
c) The time taken for the particle to return to O
Draw a diagram
13ms-1
O
A
Write out ‘suvat’
with the
information given
The particle
returns to O
when s = 0
Replace s, u and a
Simplify
The particle is at O when t = 0
seconds (to begin with) and is
at O again when t = 6.5 seconds
Rearrange
Factorise
2B
27. Kinematics of a Particle moving in a
Straight Line
You can also use 3 more formulae
linking different combination of
‘SUVAT’, for a particle moving in
a straight line with constant
acceleration
A particle is travelling along the x-axis with constant deceleration
2.5ms-2. At time t = O, the particle passes through the origin, moving
in the positive direction with speed 15ms-1. Calculate the distance
travelled by the particle by the time it returns to the origin.
15ms-1
Draw a diagram
O
X
The total distance
travelled will be double the
distance the particle
reaches from O (point X)
At X, the velocity is 0
Replace
v, u and a
Simplify
We are
calculating
s, using u, v and a
Add 5s
Divide by 5
45m is the distance from O
to X. Double it for the total
distance travelled
2B