The document discusses motion in a straight line, including key concepts like:
1. Motion can be described using frames of reference with reference points and coordinate systems to define position and time.
2. Motion can occur in one, two, or three dimensions depending on the number of coordinates needed to describe the motion.
3. Distance refers to the total path length traveled, while displacement is the directed line segment between the start and end points and is a vector quantity.
4. Speed, velocity, and acceleration are concepts that describe the rate of change of motion and can be uniform, variable, average, or instantaneous depending on whether they change over time.
This document provides definitions and explanations of key concepts related to motion, including:
1. Motion is defined as a change in an object's position over time, while rest is defined as no change in position over time. Motion and rest are relative terms depending on the frame of reference.
2. Distance is the total path length traveled by an object, while displacement is the straight-line distance between the starting and ending points of an object's motion. Displacement is a vector quantity.
3. Speed is defined as the rate of change of distance over time and is a scalar quantity. Velocity is defined as the rate of change of displacement over time and includes both magnitude and direction, making it a vector quantity
This document provides definitions and explanations of key concepts related to motion including:
1. Motion is defined as a change in an object's position over time, while rest is defined as no change in position over time. Motion and rest are relative terms depending on the frame of reference.
2. Displacement is the straight-line distance between an object's initial and final positions including direction, while distance is the total path length traveled by an object regardless of direction.
3. Speed is the rate of change of distance over time and is a scalar quantity, while velocity is the rate of change of displacement over time and is a vector quantity that includes direction.
03 MOTION IN A STRAIGHT LINE.pdf for class 11karjuna815
1. The document discusses various concepts related to motion in a straight line including speed, velocity, acceleration, equations of motion, and graphical representations.
2. Key concepts covered include the difference between speed and velocity, definitions and types of acceleration, and equations of uniformly accelerated motion derived through graphical methods.
3. Graphical analysis of position-time, velocity-time and acceleration-time relationships are presented along with examples of motion under uniform and non-uniform acceleration.
1) Motion is defined as a change in an object's position over time. It can be linear, circular, or oscillatory.
2) Mechanics studies the motion and forces on objects. It includes kinematics which describes motion, statics which considers forces on stationary objects, and dynamics which considers forces causing motion.
3) One dimensional motion involves change in one coordinate, two dimensional in two coordinates, and three dimensional in all three coordinates. Rectilinear motion follows a straight line path while circular motion follows a circular path.
Here are the key points about rate of change of velocity:
- Rate of change of velocity is also known as acceleration.
- Acceleration is a vector quantity which indicates the rate at which the velocity of an object is changing.
- The SI unit of acceleration is meter per second squared (m/s2).
- If an object's velocity is increasing with time, it has a positive acceleration. If velocity is decreasing with time, acceleration is negative.
- Acceleration can be caused by a change in the object's speed, direction of motion, or both.
- Constant acceleration means the rate of change of velocity remains the same over time. This results in a linear relationship between velocity and time
The document defines and provides examples of different types of motion including translational, rotational, and periodic motion. It discusses linear motion and distinguishes between uniform and non-uniform motion. Key physical quantities like displacement, speed, velocity, acceleration are defined. The three equations of motion relating these quantities are presented. Circular motion is also discussed.
1) The document discusses various concepts related to motion including linear motion, uniform motion, non-uniform motion, scalar and vector quantities, distance, displacement, speed, velocity, acceleration, and circular motion.
2) It provides definitions and examples for different types of motion such as translatory, rotational, and periodic motion.
3) The three equations of motion relating displacement, velocity, acceleration, and time are described.
This document provides definitions and explanations of key concepts related to motion, including:
1. Motion is defined as a change in an object's position over time, while rest is defined as no change in position over time. Motion and rest are relative terms depending on the frame of reference.
2. Distance is the total path length traveled by an object, while displacement is the straight-line distance between the starting and ending points of an object's motion. Displacement is a vector quantity.
3. Speed is defined as the rate of change of distance over time and is a scalar quantity. Velocity is defined as the rate of change of displacement over time and includes both magnitude and direction, making it a vector quantity
This document provides definitions and explanations of key concepts related to motion including:
1. Motion is defined as a change in an object's position over time, while rest is defined as no change in position over time. Motion and rest are relative terms depending on the frame of reference.
2. Displacement is the straight-line distance between an object's initial and final positions including direction, while distance is the total path length traveled by an object regardless of direction.
3. Speed is the rate of change of distance over time and is a scalar quantity, while velocity is the rate of change of displacement over time and is a vector quantity that includes direction.
03 MOTION IN A STRAIGHT LINE.pdf for class 11karjuna815
1. The document discusses various concepts related to motion in a straight line including speed, velocity, acceleration, equations of motion, and graphical representations.
2. Key concepts covered include the difference between speed and velocity, definitions and types of acceleration, and equations of uniformly accelerated motion derived through graphical methods.
3. Graphical analysis of position-time, velocity-time and acceleration-time relationships are presented along with examples of motion under uniform and non-uniform acceleration.
1) Motion is defined as a change in an object's position over time. It can be linear, circular, or oscillatory.
2) Mechanics studies the motion and forces on objects. It includes kinematics which describes motion, statics which considers forces on stationary objects, and dynamics which considers forces causing motion.
3) One dimensional motion involves change in one coordinate, two dimensional in two coordinates, and three dimensional in all three coordinates. Rectilinear motion follows a straight line path while circular motion follows a circular path.
Here are the key points about rate of change of velocity:
- Rate of change of velocity is also known as acceleration.
- Acceleration is a vector quantity which indicates the rate at which the velocity of an object is changing.
- The SI unit of acceleration is meter per second squared (m/s2).
- If an object's velocity is increasing with time, it has a positive acceleration. If velocity is decreasing with time, acceleration is negative.
- Acceleration can be caused by a change in the object's speed, direction of motion, or both.
- Constant acceleration means the rate of change of velocity remains the same over time. This results in a linear relationship between velocity and time
The document defines and provides examples of different types of motion including translational, rotational, and periodic motion. It discusses linear motion and distinguishes between uniform and non-uniform motion. Key physical quantities like displacement, speed, velocity, acceleration are defined. The three equations of motion relating these quantities are presented. Circular motion is also discussed.
1) The document discusses various concepts related to motion including linear motion, uniform motion, non-uniform motion, scalar and vector quantities, distance, displacement, speed, velocity, acceleration, and circular motion.
2) It provides definitions and examples for different types of motion such as translatory, rotational, and periodic motion.
3) The three equations of motion relating displacement, velocity, acceleration, and time are described.
This document discusses motion in a straight line, including definitions of key terms like distance, displacement, speed, velocity, uniform motion, non-uniform motion, acceleration, and equations of motion. It defines distance as the total path length traveled, displacement as the shortest distance between initial and final positions, and distinguishes between scalar and vector quantities. Graphs of distance-time and velocity-time are presented for different motion types. Equations relating velocity, displacement, time, initial velocity, acceleration, and final velocity are derived for uniformly accelerated motion.
MOTION Class IX PowerPoint Presentation Arpan Bose
1. Motion is defined as a change in position of an object over time relative to its surroundings. An object is said to be at rest if its position does not change over time relative to its surroundings.
2. Motion can be classified as translatory, rotational, or periodic. Translatory motion involves straight-line motion, rotational motion involves motion around a fixed axis, and periodic motion repeats over regular time intervals.
3. Physical quantities can be scalar or vector. Scalar quantities only require magnitude, while vector quantities require both magnitude and direction. Examples of scalars include mass and time, while examples of vectors include velocity and displacement.
Motion is one of the fundamental topics in physics and describes how everything in the universe changes position over time. Even objects that appear stationary are in motion due to larger scale movements like the Earth orbiting the sun. There are several laws that govern motion and explain changes in the speed and direction of moving objects. Equations of motion precisely define the relationships between variables like velocity, acceleration, distance, and time that are used to analyze and predict how objects will move. Motion can be linear along a straight path or involve changes in direction. While distance refers only to the length traveled, displacement considers both distance and direction of movement between two points.
This document defines and describes key concepts related to motion, including definitions of distance, displacement, speed, uniform and non-uniform motion. It also summarizes Newton's laws of motion, stating that an object at rest stays at rest unless acted upon by an unbalanced force, and that acceleration is directly proportional to net force and inversely proportional to mass. Motion can refer to the movement of objects, particles, fields, waves, probabilities and more.
this project is basically based "motion", the way it's directly or indirectly linked to us. Viewing this power point presentation will enable you to study as a whole in descriptive way.In physics, motion is a change in position of an object with respect to time. Motion is typically described in terms of displacement, distance (scalar), velocity, acceleration, time and speed.Motion of a body is observed by attaching a frame of reference to an observer and measuring the change in position of the body relative to that frame n If the position of a body is not changing with the time with respect to a given frame of reference the body is said to be at rest, motionless, immobile, stationary, or to have constant (time-invariant) position. An object's motion cannot change unless it is acted upon by a force, as described by Newton's first law. Momentum is a quantity which is used for measuring motion of an object. An object's momentum is directly related to the object's mass and velocity, and the total momentum of all objects in an isolated system (one not affected by external forces) does not change with time, as described by the law of conservation of momentum.
Hope you will like it and feedbacks are welcomed.
1. Motion refers to the change in position of an object over time. It can be described by quantities like displacement, velocity, acceleration, etc.
2. Motion can be classified as one-dimensional, two-dimensional, or three-dimensional depending on whether an object moves along a straight line, curved path, or through space.
3. Key parameters for describing one-dimensional motion include position, displacement, velocity, acceleration, distance, and speed. Displacement refers to the shortest distance between initial and final positions, while distance depends on the actual path traveled.
1. Three observers see the same object from different positions and report different positions for it, which are all correct from their perspectives due to their different frames of reference. Position is defined by a vector called the position vector that specifies distance and direction from the observer.
2. An object at rest does not change its position over time relative to a frame of reference, while a moving object does change its position over time. Rest and motion are relative terms depending on the frame of reference. One-dimensional motion involves change of only one coordinate, two-dimensional two coordinates, and three-dimensional all three coordinates changing over time.
3. A particle is the smallest unit of matter that can be described by its mass and
Motion refers to a change in an object's position over time and can be described by factors like displacement, velocity, and acceleration. There are different types of motion including uniform, non-uniform, and rest. Uniform motion means traveling equal distances in equal time intervals while non-uniform motion means traveling unequal distances in equal time or vice versa. Speed, velocity, and acceleration are also defined, with acceleration being the rate of change of an object's velocity over time. Common types of acceleration include uniform and non-uniform. Equations of motion can be used to analyze an object's motion if variables like displacement, velocity, acceleration, and time are known.
CBSE Class 9&10th Sample eBook , which helps you to understand the chapter in easy way also downaload sample papers and previous year papers and practice to solve the question on time. Download at www.misostudy.com.
This document discusses various concepts related to motion including:
1. Motion can be uniform or non-uniform. Uniform motion occurs when an object covers equal distances in equal intervals of time.
2. Displacement is the shortest distance between the initial and final position of an object, as opposed to distance which is the total path length covered.
3. Speed-time and distance-time graphs can be used to represent and analyze motion. The slope of speed-time graphs gives acceleration and areas under the graphs relate to displacement.
The document discusses key concepts in physics including motion, Newton's laws of motion, and elements of motion such as distance, displacement, speed, velocity, acceleration, and time. It also provides equations of motion and introduces concepts in quantum mechanics. Newton's three laws of motion are summarized as the first law describing objects at rest or in motion remaining as such unless acted on by an external force, the second law relating force, mass and acceleration, and the third law stating equal and opposite reaction forces.
Ekeeda Provides Online Civil Engineering Degree Subjects Courses, Video Lectures for All Engineering Universities. Video Tutorials Covers Subjects of Mechanical Engineering Degree.
This document discusses kinematics of rigid bodies, including:
- Types of rigid body motion such as translation, rotation about a fixed axis, and general plane motion.
- Translation motion is further divided into rectilinear and curvilinear types.
- Key terms related to rotation about a fixed axis like angular position, displacement, velocity, and acceleration.
- Relations between linear and angular velocity and acceleration.
- Two special cases involving rotation of pulleys - a pulley connected to a rotating block, and two coupled pulleys rotating without slip.
- Five sample problems calculating values like angular velocity and acceleration, revolutions, linear velocity and acceleration for rotating bodies.
Learn Online Courses of Subject Introduction to Civil Engineering and Engineering Mechanics. Clear the Concepts of Introduction to Civil Engineering and Engineering Mechanics Through Video Lectures and PDF Notes. Visit us: https://ekeeda.com/streamdetails/subject/introduction-to-civil-engineering-and-engineering-mechanics
This document contains a group presentation on motion by Javed Ali, Khalid Hussain, Muqadas Khursid, and Sheeera Parveen from the National University of Modern Languages in Islamabad. It defines important terms related to motion such as position, distance, displacement, speed, velocity, and acceleration. It describes different types of motion including translational, rotational, reciprocating, oscillatory, periodic, and projectile motion. Finally, it outlines Isaac Newton's three laws of motion, providing the statement and mathematical expression for each law.
This document discusses motion and related concepts like reference frames, distance, displacement, speed, velocity, and acceleration. It defines these terms and provides examples to illustrate the differences between distance and displacement, uniform and non-uniform motion, speed and velocity. Graphs showing distance-time and velocity-time relationships are also explained. Key concepts covered include how displacement accounts for direction of motion unlike distance, and how acceleration is the rate of change of velocity with respect to time.
2-1 POSITION, DISPLACEMENT, AND AVERAGE VELOCITY
After reading this module, you should be able to …
2.01 Identify that if all parts of an object move in the same direction and at the same rate, we can treat the object as if it
were a (point-like) particle. (This chapter is about the motion of such objects.)
2.02 Identify that the position of a particle is its location as
read on a scaled axis, such as an x-axis.
2.03 Apply the relationship between a particle’s
displacement and its initial and final positions.
2.04 Apply the relationship between a particle’s average
velocity, its displacement, and the time interval for that
displacement.
2.05 Apply the relationship between a particle’s average
speed, the total distance it moves, and the time interval for
the motion.
2.06 Given a graph of a particle’s position versus time,
determine the average velocity between any two particular
times.
2-1 POSITION, DISPLACEMENT, AND AVERAGE VELOCITY
After reading this module, you should be able to . . .
2.07 Given a particle’s position as a function of time,
calculate the instantaneous velocity for any particular time.
2.08 Given a graph of a particle’s position versus time, determine the instantaneous velocity for any particular time.
2.09 Identify speed as the magnitude of the instantaneous
velocity.
etc......
The document provides an overview of motion in one dimension, including key concepts such as scalars and vectors, distance and displacement, speed and velocity, and acceleration. It defines these terms and distinguishes between them. Examples of motion graphs including displacement-time graphs, velocity-time graphs, and acceleration-time graphs are presented and the slopes and areas of these graphs are related to velocity, acceleration, and displacement. Equations of motion are described for objects experiencing constant acceleration due to gravity or thrown vertically.
This document discusses various topics related to motion including:
1) Motion can be classified as one-dimensional, two-dimensional, or three-dimensional depending on the number of axes the object moves along.
2) Key concepts in three-dimensional motion include location vectors, displacement, velocity, acceleration, and equations of motion.
3) Forces obey Newton's Laws - the acceleration of an object is directly proportional to net force and inversely proportional to mass, and every action has an equal and opposite reaction.
4) Circular motion involves centripetal force which acts towards the center of the circle, and centripetal acceleration which is required to move in a circular path.
Assessment and Planning in Educational technology.pptxKavitha Krishnan
In an education system, it is understood that assessment is only for the students, but on the other hand, the Assessment of teachers is also an important aspect of the education system that ensures teachers are providing high-quality instruction to students. The assessment process can be used to provide feedback and support for professional development, to inform decisions about teacher retention or promotion, or to evaluate teacher effectiveness for accountability purposes.
This document discusses motion in a straight line, including definitions of key terms like distance, displacement, speed, velocity, uniform motion, non-uniform motion, acceleration, and equations of motion. It defines distance as the total path length traveled, displacement as the shortest distance between initial and final positions, and distinguishes between scalar and vector quantities. Graphs of distance-time and velocity-time are presented for different motion types. Equations relating velocity, displacement, time, initial velocity, acceleration, and final velocity are derived for uniformly accelerated motion.
MOTION Class IX PowerPoint Presentation Arpan Bose
1. Motion is defined as a change in position of an object over time relative to its surroundings. An object is said to be at rest if its position does not change over time relative to its surroundings.
2. Motion can be classified as translatory, rotational, or periodic. Translatory motion involves straight-line motion, rotational motion involves motion around a fixed axis, and periodic motion repeats over regular time intervals.
3. Physical quantities can be scalar or vector. Scalar quantities only require magnitude, while vector quantities require both magnitude and direction. Examples of scalars include mass and time, while examples of vectors include velocity and displacement.
Motion is one of the fundamental topics in physics and describes how everything in the universe changes position over time. Even objects that appear stationary are in motion due to larger scale movements like the Earth orbiting the sun. There are several laws that govern motion and explain changes in the speed and direction of moving objects. Equations of motion precisely define the relationships between variables like velocity, acceleration, distance, and time that are used to analyze and predict how objects will move. Motion can be linear along a straight path or involve changes in direction. While distance refers only to the length traveled, displacement considers both distance and direction of movement between two points.
This document defines and describes key concepts related to motion, including definitions of distance, displacement, speed, uniform and non-uniform motion. It also summarizes Newton's laws of motion, stating that an object at rest stays at rest unless acted upon by an unbalanced force, and that acceleration is directly proportional to net force and inversely proportional to mass. Motion can refer to the movement of objects, particles, fields, waves, probabilities and more.
this project is basically based "motion", the way it's directly or indirectly linked to us. Viewing this power point presentation will enable you to study as a whole in descriptive way.In physics, motion is a change in position of an object with respect to time. Motion is typically described in terms of displacement, distance (scalar), velocity, acceleration, time and speed.Motion of a body is observed by attaching a frame of reference to an observer and measuring the change in position of the body relative to that frame n If the position of a body is not changing with the time with respect to a given frame of reference the body is said to be at rest, motionless, immobile, stationary, or to have constant (time-invariant) position. An object's motion cannot change unless it is acted upon by a force, as described by Newton's first law. Momentum is a quantity which is used for measuring motion of an object. An object's momentum is directly related to the object's mass and velocity, and the total momentum of all objects in an isolated system (one not affected by external forces) does not change with time, as described by the law of conservation of momentum.
Hope you will like it and feedbacks are welcomed.
1. Motion refers to the change in position of an object over time. It can be described by quantities like displacement, velocity, acceleration, etc.
2. Motion can be classified as one-dimensional, two-dimensional, or three-dimensional depending on whether an object moves along a straight line, curved path, or through space.
3. Key parameters for describing one-dimensional motion include position, displacement, velocity, acceleration, distance, and speed. Displacement refers to the shortest distance between initial and final positions, while distance depends on the actual path traveled.
1. Three observers see the same object from different positions and report different positions for it, which are all correct from their perspectives due to their different frames of reference. Position is defined by a vector called the position vector that specifies distance and direction from the observer.
2. An object at rest does not change its position over time relative to a frame of reference, while a moving object does change its position over time. Rest and motion are relative terms depending on the frame of reference. One-dimensional motion involves change of only one coordinate, two-dimensional two coordinates, and three-dimensional all three coordinates changing over time.
3. A particle is the smallest unit of matter that can be described by its mass and
Motion refers to a change in an object's position over time and can be described by factors like displacement, velocity, and acceleration. There are different types of motion including uniform, non-uniform, and rest. Uniform motion means traveling equal distances in equal time intervals while non-uniform motion means traveling unequal distances in equal time or vice versa. Speed, velocity, and acceleration are also defined, with acceleration being the rate of change of an object's velocity over time. Common types of acceleration include uniform and non-uniform. Equations of motion can be used to analyze an object's motion if variables like displacement, velocity, acceleration, and time are known.
CBSE Class 9&10th Sample eBook , which helps you to understand the chapter in easy way also downaload sample papers and previous year papers and practice to solve the question on time. Download at www.misostudy.com.
This document discusses various concepts related to motion including:
1. Motion can be uniform or non-uniform. Uniform motion occurs when an object covers equal distances in equal intervals of time.
2. Displacement is the shortest distance between the initial and final position of an object, as opposed to distance which is the total path length covered.
3. Speed-time and distance-time graphs can be used to represent and analyze motion. The slope of speed-time graphs gives acceleration and areas under the graphs relate to displacement.
The document discusses key concepts in physics including motion, Newton's laws of motion, and elements of motion such as distance, displacement, speed, velocity, acceleration, and time. It also provides equations of motion and introduces concepts in quantum mechanics. Newton's three laws of motion are summarized as the first law describing objects at rest or in motion remaining as such unless acted on by an external force, the second law relating force, mass and acceleration, and the third law stating equal and opposite reaction forces.
Ekeeda Provides Online Civil Engineering Degree Subjects Courses, Video Lectures for All Engineering Universities. Video Tutorials Covers Subjects of Mechanical Engineering Degree.
This document discusses kinematics of rigid bodies, including:
- Types of rigid body motion such as translation, rotation about a fixed axis, and general plane motion.
- Translation motion is further divided into rectilinear and curvilinear types.
- Key terms related to rotation about a fixed axis like angular position, displacement, velocity, and acceleration.
- Relations between linear and angular velocity and acceleration.
- Two special cases involving rotation of pulleys - a pulley connected to a rotating block, and two coupled pulleys rotating without slip.
- Five sample problems calculating values like angular velocity and acceleration, revolutions, linear velocity and acceleration for rotating bodies.
Learn Online Courses of Subject Introduction to Civil Engineering and Engineering Mechanics. Clear the Concepts of Introduction to Civil Engineering and Engineering Mechanics Through Video Lectures and PDF Notes. Visit us: https://ekeeda.com/streamdetails/subject/introduction-to-civil-engineering-and-engineering-mechanics
This document contains a group presentation on motion by Javed Ali, Khalid Hussain, Muqadas Khursid, and Sheeera Parveen from the National University of Modern Languages in Islamabad. It defines important terms related to motion such as position, distance, displacement, speed, velocity, and acceleration. It describes different types of motion including translational, rotational, reciprocating, oscillatory, periodic, and projectile motion. Finally, it outlines Isaac Newton's three laws of motion, providing the statement and mathematical expression for each law.
This document discusses motion and related concepts like reference frames, distance, displacement, speed, velocity, and acceleration. It defines these terms and provides examples to illustrate the differences between distance and displacement, uniform and non-uniform motion, speed and velocity. Graphs showing distance-time and velocity-time relationships are also explained. Key concepts covered include how displacement accounts for direction of motion unlike distance, and how acceleration is the rate of change of velocity with respect to time.
2-1 POSITION, DISPLACEMENT, AND AVERAGE VELOCITY
After reading this module, you should be able to …
2.01 Identify that if all parts of an object move in the same direction and at the same rate, we can treat the object as if it
were a (point-like) particle. (This chapter is about the motion of such objects.)
2.02 Identify that the position of a particle is its location as
read on a scaled axis, such as an x-axis.
2.03 Apply the relationship between a particle’s
displacement and its initial and final positions.
2.04 Apply the relationship between a particle’s average
velocity, its displacement, and the time interval for that
displacement.
2.05 Apply the relationship between a particle’s average
speed, the total distance it moves, and the time interval for
the motion.
2.06 Given a graph of a particle’s position versus time,
determine the average velocity between any two particular
times.
2-1 POSITION, DISPLACEMENT, AND AVERAGE VELOCITY
After reading this module, you should be able to . . .
2.07 Given a particle’s position as a function of time,
calculate the instantaneous velocity for any particular time.
2.08 Given a graph of a particle’s position versus time, determine the instantaneous velocity for any particular time.
2.09 Identify speed as the magnitude of the instantaneous
velocity.
etc......
The document provides an overview of motion in one dimension, including key concepts such as scalars and vectors, distance and displacement, speed and velocity, and acceleration. It defines these terms and distinguishes between them. Examples of motion graphs including displacement-time graphs, velocity-time graphs, and acceleration-time graphs are presented and the slopes and areas of these graphs are related to velocity, acceleration, and displacement. Equations of motion are described for objects experiencing constant acceleration due to gravity or thrown vertically.
This document discusses various topics related to motion including:
1) Motion can be classified as one-dimensional, two-dimensional, or three-dimensional depending on the number of axes the object moves along.
2) Key concepts in three-dimensional motion include location vectors, displacement, velocity, acceleration, and equations of motion.
3) Forces obey Newton's Laws - the acceleration of an object is directly proportional to net force and inversely proportional to mass, and every action has an equal and opposite reaction.
4) Circular motion involves centripetal force which acts towards the center of the circle, and centripetal acceleration which is required to move in a circular path.
Assessment and Planning in Educational technology.pptxKavitha Krishnan
In an education system, it is understood that assessment is only for the students, but on the other hand, the Assessment of teachers is also an important aspect of the education system that ensures teachers are providing high-quality instruction to students. The assessment process can be used to provide feedback and support for professional development, to inform decisions about teacher retention or promotion, or to evaluate teacher effectiveness for accountability purposes.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
How to Build a Module in Odoo 17 Using the Scaffold MethodCeline George
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
How to Add Chatter in the odoo 17 ERP ModuleCeline George
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
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A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
1. MOTION IN A STRAIGHT LINE
1. Branches of Physics
2. Concept of a Point Object, Reference Point and Frame of Reference
3. Origin of Position and Time; Rest and Motion – Relative Terms
4. Motion in One, Two and Three Dimension
5. Motion in a Straight Line – Distance and Displacement, Scalar & Vector
6. Speed - Uniform, Variable, Average and Instantaneous Speed
7. Velocity - Uniform, Variable, Average(Graph) and Instantaneous(Graph)
8. Difference between Speed and Velocity
9. Uniform Motion in a Straight Line
10.Position-Time Graph and Velocity-Time Graph of Uniform Motion
11.Non-uniform Motion – Acceleration (Uniform, Non-Uniform)
12.Position-Time Graph and Velocity-Time Graph of Non-Uniform Motion
13.Equations of Motion – Normal(1st,2nd,3rd) / Graphical(1st,2nd,3rd) /
Calculus(1st,2nd,3rd) Method of Derivation
14.Relative Velocity and Graphs
Next
2. Mechanics
Mechanics is a branch of physics that deals with the motion of a body due to
the application of force.
The two main branches of mechanics are:
(a) Statics and
(b) Dynamics
Statics
Statics is the study of the motion of an object under the effect of forces in
equilibrium.
Dynamics
Dynamics is the study of the motion of the objects by taking into account the
cause of their change of states (state of rest or motion).
Dynamics is classified into (i) Kinematics and (ii) Kinetics
Kinematics
The study of the motion of the objects without taking into account the cause
of their motion is called kinematics.
Kinetics
Kinetics is the study of motion which relates to the action of forces causing
the motion and the mass that is moved.
Home Next Previous
3. Concept of a Point Object
In mechanics, a particle is a geometrical mass point or a material body of
negligible dimensions. It is only a mathematical idealization.
Examples:
In practice, the nearest approach to a particle is a body, whose size is much
smaller than the distance or the length involved. Home Next Previous
4. POSITION, PATH LENGTH AND DISPLACEMENT
Reference Point
Consider a rectangular coordinate system consisting of three mutually
perpendicular axes, labeled X-, Y-, and Z- axes. The point of intersection of
these three axes is called origin (O) and serves as the reference point. The
coordinates (x, y, z) of an object describe the position of the object with
respect to this coordinate system.
Frame of reference
The coordinate system along with a clock to measure
the time constitutes a frame of reference.
Positive direction
The positive direction of an axis is in the direction
of increasing numbers (coordinates).
Negative direction
The negative direction of an axis is in the direction
of decreasing numbers (coordinates).
X
Z
Y
O
Home Next Previous
5. While describing motion, we use reference point or origin
w.r.t. which the motion of other bodies are observed.
We can use any object as reference point. For example, a
car at rest or in motion can be used as reference point.
When you travel in a bus or train you can see the trees,
buildings and the poles moving back.
To a tree, you are moving forward and to you, the trees are
moving back.
Both, you and the trees, can serve as reference point but
motion can not be described without reference point.
What effect do you get when you play video game involving
car racing?
Home Next Previous
6. 1. The distance measured to the right of the origin of the position axis is
taken positive and the distance measured to the left of the origin is taken
negative.
2. The origin for position can be shifted to any point on the position axis.
3. The distance between two points on position-axis is not affected due to
the shift in the origin of position-axis.
Origin, unit and direction of position measurement of an object
-60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 (m)
+X
-X
Origin, unit and sense of passage of time
1. The time measured to the right of the origin of the time-axis is taken
positive and the time measured to the left of the origin is taken negative.
2. The origin of the time-axis can be shifted to any point on the time-axis.
3. The negative time co-ordinate of a point on time-axis means that object
reached that point a time that much before the origin of the time-axis i.e. t = 0.
4. The time interval between two points on time-axis is not affected due to the
shift in the origin of time-axis.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 (s)
+t
-t
Home Next Previous
7. When the same point is chosen as origins for position and time:
O A B C
x = 0 x = 30 km x = 40 km x = 55 km
t = 0 t = 6 h t = 8 h t = 11 h
When the different points are chosen as origins for position
and time:
O A B C
x = - 40 km x = -10 km x = 0 km x = 15 km
t = -6 h t = 0 t = 2 h t = 5 h
Origin for position and time
Origin for time Origin for position
Home Next Previous
8. Rest and Motion
A ball is at rest w.r.t. a stationary man.
A car is at rest w.r.t. a stationary man.
A ball is moving w.r.t. a stationary man.
A car is moving w.r.t. a stationary man.
Home Next Previous
9. Rest
A body is said to be at rest if its position remains constant with respect to
its surroundings or frame of reference.
Examples: Mountains, Buildings, etc.
Motion
A body is said to be in motion if its position is changing with respect to its
surroundings or frame of reference.
Examples: 1. Moving cars, buses, trains, cricket ball, etc.
2. All the planets revolving around the Sun
3. Molecules of a gas in motion above 0 K
Rest and Motion are relative terms:
An object which is at rest can also be in motion simultaneously.
Eg. The passengers sitting in a moving train are at rest w.r.t. each other but
they are also in motion at the same time w.r.t. the objects like trees,
buildings, etc.
Home Next Previous
10. Rest and Motion are Relative Terms
Car is moving w.r.t. stationary man.
Car is moving w.r.t. stationary man.
Home Next Previous
11. Rest and Motion are Relative Terms
Both the cars are at rest w.r.t. stationary man.
Both the cars are moving w.r.t. a stationary man.
Both the cars are at rest w.r.t. each other.
Home Next Previous
12. In the examples of motion of ball and car, man is considered to be
at rest (stationary).
But, the man is standing on the Earth and the Earth itself moves
around the Sun as well as rotates about its own axis.
Therefore, man is at rest w.r.t. the Earth but is rotating and
revolving around the Sun.
That is why rest and motion are relative terms !
Rest and Motion are Relative Terms – How?
Home Next Previous
13. A ship is sailing in the ocean. Man-A in the ship is running on the board in
the direction opposite to the direction of motion of the ship. Man-B in
the ship is standing and watching the Man-A.
Analyse the following cases to understand motion and rest !
1. Man-A w.r.t. Man-B
2. Man-A w.r.t. ship
3. Man-B w.r.t. ship
4. Ship w.r.t. still water
5. Man-A w.r.t. still water
6. Man-B w.r.t. still water
7. Ocean w.r.t. the Earth
8. Ocean w.r.t. the Sun
9. Earth w.r.t. the Sun
10.Ship w.r.t. the Sun
11.The Sun w.r.t. Milky Way Galaxy
12. Milky Way Galaxy w.r.t. other galaxies
Your imagination should not ever stop ! Home Next Previous
14. MOTION IN ONE, TWO OR THREE DIMENSIONS
One Dimensional Motion
The motion of the object is said to be one dimensional if only one of the three
coordinates is required to be specified with respect to time. It is also known
as rectilinear motion.
In such a motion the object moves in a straight line.
Example: A train moving in straight track, a man walking in a narrow, leveled
road, etc.
Two Dimensional Motion
The motion of the object is said to be two dimensional if two of the three
coordinates are required to be specified with respect to time.
In such a motion the object moves in a plane.
Example: Ant moving on a floor, a billiard ball moving on a billiard table, etc.
Three Dimensional Motion
The motion of the object is said to be three dimensional if all the three
coordinates are required to be specified with respect to time.
Such a motion takes place in space.
Example: A flying airplane, bird, kite, etc.
Home Next Previous
15. N
5 km
2 km
5 km
Distance travelled is 7 km.
Distance travelled is 10 km.
Path
The line joining the successive positions of a moving body is called its path.
The length of the actual path between the initial and final position gives the
distance travelled by the body. Distance is a scalar.
Motion in a Straight Line
Illustration
Home Next Previous
16. N
5 km
2 km
5 km
Displacement is 6.57 km in the direction shown by the arrow
mark.
Displacement is 0 km.
Displacement
Displacement is the directed line segment joining the initial and final positions
of a moving body. It is a vector.
Illustration
Home Next Previous
17. If a body changes from one position x1 to another position x2, then the
displacement Δx in time interval Δt = t2 – t1, is Δx = x2 – x1
Conclusions about displacement
1. The displacement is a vector quantity.
2. The displacement has units of length.
3. The displacement of an object in a given time interval can be
positive, zero or negative.
4. The actual distance travelled by an object in a given time interval
can be equal to or greater than the magnitude of the
displacement.
5. The displacement of an object between two points does not tell
exactly how the object actually moved between those points.
6. The displacement of a particle between two points is a unique
path, which can take the particle from its initial to final position.
7. The displacement of an object is not affected due to the shift in
the origin of the position-axis.
Home Next Previous
18. Scalar
Scalar quantity is a physical quantity which has magnitude only.
Eg.: Length, Mass, Time, Speed, Energy, etc.
Vector
Vector quantity is a physical quantity which has both magnitude as well as
direction.
Eg.: Displacement, Velocity, Acceleration, Momentum, Force, etc.
S. No. Distance Displacement
1
2
Distance is a scalar quantity. Displacement is a vector quantity.
Distance travelled by a
moving body cannot be zero.
Final displacement of a moving
body can be zero.
A C
B
Distance
Home Next Previous
19. Speed
The time rate of change of distance of a particle is called speed.
Speed =
Distance travelled
Time taken
or v =
s
t
Note:
1. Speed is a scalar quantity.
2. Speed is either positive or zero but never negative.
3. Speed of a running car is measured by ‘speedometer’.
4. Speed is measured in
i) cm/s (cm s-1) in cgs system of units
ii) m/s (m s-1) in SI system of units and
iii) km/h (km.p.h., km h-1) in practical life when distance and time
involved are large.
Home Next Previous
20. Uniform Speed
A particle or a body is said to be moving with uniform speed, if it covers
equal distances in equal intervals of time, howsoever small these intervals
may be.
Variable Speed
A particle or a body is said to be moving with variable speed, if it covers
unequal distances in equal intervals of time, howsoever small these
intervals may be.
Average Speed
When a body moves with variable speed, the average speed of the body
is the ratio of the total distance traveled by it to the total time taken.
Average speed =
Total distance travelled
Total time taken
or vav =
stot
ttot
Home Next Previous
21. Instantaneous Speed
When a body is moving with variable speed, the speed of the body at any
instant is called instantaneous speed.
If a particle covers the 1st half of the total distance with a speed ‘a’ and the
second half with a speed ‘b’, then
If a particle covers 1st 1/3rd of a distance with a speed ‘a’, 2nd 1/3rd of the
distance with speed ‘b’ and 3rd 1/3rd of the distance with speed ‘c’, then
vav =
2ab
a + b
vav =
3abc
ab + bc + ca
Position -Time Graph
Time t (s)
O Time t (s)
O Time t (s)
O
Stationary object
An object in uniform
motion
An object in non-uniform
motion Home Next Previous
22. Velocity
The time rate of change of displacement of a particle is called velocity.
Velocity =
Displacement
Time taken
or v =
s
t
1 m/s = km/h
18
5
1 km/h = m/s
5
18
Note:
1. Velocity is a vector quantity.
2. Direction of velocity is the same as the direction of displacement of the
body.
3. Velocity can be either positive, zero or negative.
4. Velocity can be changed in two ways:
i) by changing the speed of the body or
ii) by keeping the speed constant but by changing the direction.
5. Velocity is measured in
i) cm/s (cm s-1) in cgs system of units
ii) m/s (m s-1) in SI system of units and
iii) km/h (km.p.h., km h-1) in practical life when
distance and time involved are large. Home Next Previous
23. Average Velocity
When a body moves with variable velocity, the average velocity of the body is
the ratio of the total (net) displacement covered by it to the total time taken.
Average velocity =
Net displacement
Total time taken
or
vav =
stot
ttot
For a body moving with uniform acceleration, vav =
2
u + v
Average velocity is also defined as the change in position or displacement
(Δx) divided by the time intervals (Δt), in which the displacement occurs:
vav =
x2 – x1
t2 – t1
or vav =
Δx
Δt
Note: No effort or force is required to move the body with uniform velocity.
Uniform Velocity
A particle or a body is said to be moving with uniform velocity, if it covers
equal displacements in equal intervals of time, howsoever small these
intervals may be.
Variable Velocity
A particle or a body is said to be moving with variable velocity, if its speed or
its direction or both changes with time.
Home Next Previous
24. a) If a particle undergoes a displacement s1 along a straight line in time t1
and a displacement s2 in time t2 in the same direction, then
b) If a particle undergoes a displacement s1 along a straight line with velocity
v1 and a displacement s2 with velocity v2 in the same direction, then
c) If a particle travels first half of the displacement along a straight line with
velocity v1 and the next half of the displacement with velocity v2 in the same
direction, then
d) If a particle travels for a time t1 with velocity v1 and for a time t2 with
velocity v2 in the same direction, then
e) If a particle travels first half of the time with velocity v1 and the next half
of the time with velocity v2 in the same direction, then
vav =
s1 + s2
t1 + t2
vav =
(s1+s2) v1 v2
s1v2 + s2 v1
vav =
2 v1 v2
v1 + v2
vav =
V1t2 + v2 t2
t1 + t2
vav =
v1 + v2
2
(in the case (b) put s1 = s2)
(in the case (d) put t1 = t2)
Home Next Previous
25. Time t (s)
O Time t (s)
O Time t (s)
O
x – t graph for
stationary object
x – t graph for an
object with +ve velocity
x – t graph for an
object with -ve velocity
Time t (s)
O
The slope of P1P2 gives
average velocity.
x1
t2
x2
t1
P1
P2
Average Velocity
Uniform Velocity
Home Next Previous
26. Difference between Speed and Velocity
Speed Velocity
1. Speed is the time rate of change of
distance of a body.
1. Velocity is the time rate of
change of displacement of a body.
2. Speed tells nothing about the
direction of motion of the body.
2. Velocity tells the direction of
motion of the body.
4. Speed of the body can be
positive or zero.
4. Velocity of the body can be
positive, zero or negative.
3. Speed is a scalar quantity. 3. Velocity is a vector quantity.
5. Average speed of a moving
body can never be zero.
5. Average velocity of a moving
body can be zero.
Home Next Previous
27. Instantaneous Velocity
When a body is moving with variable velocity, the velocity of the body at any
instant is called instantaneous velocity.
The velocity at an instant is defined as the
limit of the average velocity as the time
interval Δt becomes infinitesimally small.
Suppose we want to calculate the
instantaneous velocity at the point P
at an instant t.
Time t (s)
O
x1
t4
x2
t3
P3
P4
P1
P2
t t2
t1
x4
x3
P
The slope of P1P2 at t1 and t2 with intervals
of Δt from t, (i.e. t1 = t- Δt and t2 = t+ Δt)
gives the average velocity at P.
The slope of P3P4 at t3 and t4 with intervals of Δt/2 from t, (i.e. t3 = t- Δt/2 and
t4 = t+Δt/2) gives the average velocity at P which is the closer value to the
instantaneous velocity.
Proceeding this way, Δt may be gradually reduced to approach zero,
i.e. Δt → 0 to get the actual value of the instantaneous velocity.
Though average speed over a finite interval of time is greater than or equal to
the magnitude of the average velocity, instantaneous speed at an instant is
equal to the magnitude of the instantaneous velocity at that instant. Why so?
v =
Δx
Δt
lim
Δt→0
dx
dt
v =
or
Home Next Previous
28. Uniform Motion in a Straight Line
A body is said to be in uniform motion, if it covers equal displacements in
equal intervals of time, however small these time intervals may be.
Formula for uniform motion
At t=0 At t=t1 At t=t2
O A B C
Suppose the origin of the position axis is point O and the origin for time
measurement is taken as the instant, when object is at point A such that
OA = x0.
If at time t1, the object moving with velocity v is at point B such that OB = x1,
then
x1 = x0 + vt1 ………..(1)
Similarly, if at time t2, the object is at point C such that OC = x2,
then x2 = x0 + vt2 ………..(2)
From equations (1) and (2), x2 – x1 = v(t2 – t1) and
x1
x2
v =
x2 – x1
t2 – t1
x0
Home Next Previous
29. The following points are true for Uniform Motion:
1. Generally, the displacement may or may not be equal to the actual
distance covered by an object. However, when uniform motion takes
place along a straight line in a given direction, the magnitude of the
displacement is equal to the actual distance covered by the object.
2. The velocity of uniform motion is same for different choices of t1 and t2.
3. The velocity of uniform motion is not affected due to the shift of the
origin.
4. The positive value of velocity means object is moving towards right of
the origin, while the negative velocity means the motion is towards the
left of the origin.
5. For an object to be in uniform motion, no cause or effort, i.e. no force is
required.
6. The average and instantaneous velocity in a uniform motion are always
equal, as the velocity during uniform motion is same at each point of the
path or at each instant.
Home Next Previous
30. Position - Time Graph: (Uniform motion)
Time (s)
X2
X1
x0
O
t1 t2
B
A
C
Slope of the position-time graph gives the velocity of uniform motion.
v = slope of AB =
BC
AC
v =
x2 – x1
t2 – t1
or
Home Next Previous
31. Velocity -Time Graph: (Uniform motion)
Area under velocity-time graph gives the displacement of the body in
uniform motion.
x2 – x1 = area ABCD = v (t2 – t1 )
v
O
A B
D C
Time (s)
t1 t2
Home Next Previous
32. NON-UNIFORM MOTION
The particle is said to have non-uniform motion if it covers unequal
displacements in equal intervals of time, however small these time intervals
may be.
Acceleration
If the velocity of a body changes either in magnitude or in direction or both,
then it is said to have acceleration.
For a freely falling body, the velocity changes in magnitude and hence it has
acceleration.
For a body moving round a circular path with a uniform speed, the velocity
changes in direction and hence it has acceleration.
For a projectile, whose trajectory is a parabola, the velocity changes in
magnitude and in direction, and hence it has acceleration.
The acceleration and velocity of a body need not be in the same direction.
Eg.: A body thrown vertically upwards.
Home Next Previous
33. For a body moving with uniform acceleration,
the average velocity is
A body can have zero velocity and non-zero acceleration.
Eg.: For a particle projected vertically up, velocity at the highest point is
zero, but acceleration is -g.
If a body has a uniform speed, it may have acceleration.
Eg.: Uniform circular motion
If a body has uniform velocity, it has no acceleration.
When a body moves with uniform acceleration along a straight line and has
a distance ‘x’ travelled in the nth second, in the next second it travels a
distance x + a, where ‘a’ is the acceleration.
Acceleration of free fall in vacuum is uniform and is called acceleration due
to gravity (g) and it is equal to 980 cms-2 or 9.8 ms-2.
vav =
u + v
2
Home Next Previous
34. Acceleration of a particle is defined as the time rate of change of its velocity.
or
The acceleration of a particle at any instant or at any point is called
instantaneous acceleration.
or or
Note:
1. Acceleration is a vector quantity.
2. Direction of acceleration is the same as the direction of velocity of the
body.
3. Acceleration can be either positive, zero or negative.
4. Acceleration of a body is zero when it moves with uniform velocity.
5. Acceleration is measured in
i) cm/s2 (cm s-2) in cgs system of units
ii) m/s2 (m s-2) in SI system of units and
iii) km/h2 (km h-2) in practical life when distance and time involved are
large.
aav =
v2 – v1
t2 – t1
aav =
Δv
Δt
a =
Δv
Δt
lim
Δt→0
dv
dt
a =
d2s
dt2
a =
Home Next Previous
35. Eg.2:
The motion of a sliding block on a
smooth inclined plane is uniformly
accelerated motion.
Uniform Acceleration
A body has uniform acceleration if its
velocity changes at a uniform rate.
If equal changes of velocity take place
in equal intervals of time, however small
these intervals may be, then the body is
said to be in uniform acceleration.
or
Eg.1:
The motion of a freely
falling body is
uniformly accelerated
motion.
Home Next Previous
36. Non-uniform Acceleration
A body is said to be moving with non-uniform acceleration, if its velocity
increases by unequal amounts in equal intervals of time.
A body has non-uniform acceleration if its velocity changes at a non-
uniform rate.
or
Eg.:
The motion of a car on a crowded city road. Its speed (velocity) changes
continuously.
Retardation or Deceleration or Negative Acceleration
A body is said to be retarded if its velocity decreases w.r.t. time.
A car is decelerating to come to a halt. Home Next Previous
37. Position - Time Graph
Uniformly decelerated
(Negative acceleration)
Time t (s) Time t (s)
Uniform motion
(Zero acceleration)
Time t (s)
Uniformly accelerated
(Positive acceleration)
Home Next Previous
38. Velocity - Time Graph (Uniformly accelerated / decelerated)
Time (s)
v0
v
O t Time (s)
v0
v
O t
Time (s)
-v0
-v
O
t t2
t1
Time (s)
v0
-v
O
Motion in positive direction
with positive acceleration
Motion in positive direction
with negative acceleration
Motion in negative direction
with negative acceleration
Motion with negative acceleration.
B/n 0 & t1 in positive x-axis and
b/n t1 & t2 in negative x-axis
Home Next Previous
39. KINEMATIC EQUATIONS OF UNIFORMLY ACCELERATED MOTION
Consider a body moving with initial velocity ‘v0’ accelerates at uniform rate
‘a’. Let ‘v’ be the final velocity after time ‘t’ and ‘x’ be the displacement.
v0 v
a
t
We know that:
a =
v - v0
t
Cross multiplying, v – v0 = at
or v = v0 + at
The equation v = v0 + at is known as the first equation of motion.
First equation of motion
Acceleration =
Time taken
Final velocity - Initial velocity
x
Home Next Previous
40. we get
vav =
v0 + v
2
or
The equation x = v0 t + ½ at2 is known as the second equation of motion.
Second equation of motion
Average velocity =
2
Initial velocity + Final velocity
Distance travelled = Average velocity x Time
From the first equation of motion we have, v = v0 + at
Substituting for v in equation (1),
(1)
x =
(v0 + v)
2
t
x =
(v0 + v0 + at)
2
t
x =
(2v0 + at)
2
t
or x =
2v0 t + at2
2
or x = v0 t + ½ at2
Home Next Previous
41. Third equation of motion
From the first equation of motion we have,
v – v0 = at
We know that: vav =
v0 + v
2
or v0 + v = 2vav
(1)
or v + v0 = 2vav (2)
Multiplying eqns. (1) and (2), we get
v2 - v0
2 = 2atvav
v2 - v0
2 = 2ax
or vav t = x
or v2 = v0
2 + 2ax
The equation v2 = v0
2 + 2ax is known as the third equation of motion.
Home Next Previous
42. KINEMATICEQUATIONS OF UNIFORMLY ACCELERATED MOTION
BY GRAPHICAL METHOD
First equation of motion
Acceleration =
Time taken for change
Change in velocity
O C
B
v
v0
E
A D
Time (s)
t
a =
BD
AD
a =
AE
OC
a =
OE - OA
OC
a =
v - v0
t
v – v0 = at
or v = v0 + at
v – v0
Home Next Previous
43. Second equation of motion
The area of trapezium OABC gives
the distance travelled.
x = ½ x OC x (OA + CB)
x = ½ t (v0 + v)
x = ½ t (v0 + v0 + at)
x = ½ (2v0t + at2)
x = v0t + ½ at2
Time (s)
O C
B
v E
A D
t
v0
Home Next Previous
44. Third equation of motion
The area of trapezium OABC gives
the distance travelled.
x = ½ x OC x (OA + CB)
x = ½ x t x (v0 + v)
(v + v0) =
2x
t
From the first equation of motion we have,
(v – v0) = at (2)
(1)
Multiplying eqns. (1) and (2), we get
v2 - v0
2 = 2ax
or v2 = v0
2 + 2ax
Time (s)
O C
B
v
v0
E
A D
t
Home Next Previous
45. Equations of motion of a freely falling body
In case of freely falling body, a = g and x = h
Therefore, v = v0 + gt
h = v0 t + ½ gt2
v2 = v0
2 + 2gh
If the position co-ordinate is non-zero at t=0, say ‘x0’,
then
v = v0 + at
x – x0 = v0t + ½ at2
v2 = v0
2 + 2a(x – x0)
Home Next Previous
46. Equations of motion (In terms of Calculus)
1) a = dv / dt
or dv = a dt
dv = a dt
v0
v
0
t
dv = a dt
v0
v
0
t
(since a is constant (uniform))
v - v0 = at
or v = v0 + at
Integrating both sides,
Home Next Previous
47. 2) v = dx / dt
dx = v dt
But, v = v0 + at
dx = (v0 + at) dt
dx =
x0
x
0
t
(v0 + at) dt
dx =
x0
x
0
t
v0 dt + at dt
0
t
dx = v0
x0
x
0
t
dt + t dt
0
t
a
x – x0 = v0t + ½ at2
Integrating both sides,
Home Next Previous
48. 3) a =
dv
dt
a =
dv
dx
x
dx
dt
a =
dv
dx
v
v dv = a dx
Integrating both sides,
a dx
x0
x
v dv =
v0
v
(since a is constant (uniform))
dx
x0
x
v dv = a
v0
v
½ (v2 – v0
2) = a(x – x0)
(v2 – v0
2) = 2a(x – x0)
Home Next Previous
49. Relative Velocity
Relative velocity of an object A with respect to another object B, is the rate
at which object A changes its position with respect to object B.
If vA and vB be the velocities of object A and B respectively, then relative
velocity of A w.r.t. B is vAB = vA - vB
Similarly, relative velocity of B w.r.t. A is vBA = vB - vA
Let us consider two objects A and B moving uniformly with velocities vA
and vB in one direction. Let xA(0) and xB(0) be the positions of the objects
at t = 0 from the origin O. Therefore the positions of two objects after time
t will be given by
xA(t) = xA(0) + vAt
and xB(t) = xB(0) + vBt
xB(t) - xA(t) = [xB(0) - xA(0)] + (vB - vA) t
where xB(t) - xA(t) is relative displacement at time t and
xB(0) - xA(0) is relative displacement at time t0.
Then, (vB - vA) is the relative velocity of B w.r.t. A
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50. Special Cases
1) When the two objects move with
equal velocities
2) When the two objects move with unequal velocities
i) When vA > vB
ii) When vA < vB
t (s)
xB(0)
xA(0)
x(m)
O
t (s)
xB(0)
xA(0)
x(m)
O
x(m)
t (s)
Meeting time
Meeting Position
xB(0)
xA(0)
O
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51. Acknowledgement
1. Physics Part I for Class XI by NCERT
2. Body of the car from net
3. Walking man from the net
]
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