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.
Uniformly Accelerated Motion and Free Fall Motion_NOTES.pptxALVINMARCDANCEL2
An object is in Free-Fall when the only force acting on the object is the Force of Gravity, however, we haven’t defined
Force much less the Force of Gravity, so, until we have defined the Force of Gravity, we have a slightly different definition.
An object is in Free-Fall when:
- It is not touching any other objects♥
- There is no air resistance (it’s in the vacuum we can breathe)
We are now in the vacuum that we can breathe and will be for the remainder of this class, unless otherwise stated.
Common Misconception: For some reason people think the word “fall” in Free-Fall means that the object must be going
down. This is absolutely, not true. An object thrown upward is in Free-Fall from the moment it leaves the persons hand
until it touches the ground.
This ppt was created by Dr Beka a lecture from Ekwendeni College of Health Sciences (ECoHS) Ekwendeni Mzimba Malawi. It is understandable and easy to read for students who are studying clinical medicine
Ph2A Win 2020 Numerical Analysis Lab
Max Yuen
Mar 2020
(use g = 9.8m/s2 for all problems.)
Background
Many physics problems cannot be solved directly by hand or analytically. We resort to numerical
methods to give us approximations to the problem. In this lab you will learn the Euler method,
which allows you to solve Newton’s laws of motion. This is done by treating the velocity as a
piecewise linear function with many time intervals and during interval the acceleration is assumed
to be uniform. This allows us to use the kinematic equations we learned about in the first half
of the class to approximate the motion. If we choose to partition the motion into smaller time
intervals, the approximation becomes much better since the differences between adjacent intervals
become smaller. In this lab, this numerical analysis method will be applied to the motion of a
falling object under the influence of gravity and drag force. If you are adventurous, you can even
try to extend this to 2D and compute the realistic trajectory of a baseball. You might even try
some other problems, such as a mass attached to a spring.
Euler’s Method Foundations
This method is well suited for problems where the acceleration is a function of the velocity, as in
the case of a falling object under the influence of gravity and drag:
a = f(v) (1)
Falling object with drag force
The model for drag fits the prescription for using Euler’s method since the net force on a falling
object with drag is given by:
ma = −mg −FD (2)
ma = −mg −
1
2
ρairACDv
2 · sgn(v) (3)
a = −g
(
1 +
ρairACDv
2 · sgn(v)
2mg
)
(4)
a = f(v) ← Equation of Motion (5)
where m is the mass of the falling object, a is the acceleration of the object (which is positive when
pointed up), ρair is the density of air (about 1.29 ·10−3kg/m3), A is the cross-sectional area, CD is
the drag coefficient, v is the object’s velocity, and sgn(v) is the signum function which returns the
sign of the argument. The second signum function is there to guarantee that the direction of the
drag force is always in the opposite direction of the velocity function. Note that we see that the
acceleration is an explicit function of v, which sort of makes this a chicken or egg problem. This is
because we need a to get v, but to get a we need v, so which one do we compute first? Hold that
thought. We’ll talk more on how to program this in EXCEL or Google Sheets later.
1
Figure 1: FBD for an object falling under the pull of gravity and resistance by drag force
Terminal Velocity
In lecture, we talked about how after waiting for some time, if the object started at rest the
speed will increase and the drag force will also become larger and eventually balance out with the
gravitational force. When this happens, we have reached terminal velocity vterm = −v. This can
be solved by setting a = 0:
0 = −mg −
1
2
ρairACDv
2 · sgn(v) (6)
2mg = ρairACDv
2
term (7)
→ vterm =
√
2mg
ρairACD
(8)
Using this definition for the terminal ...
Uniformly Accelerated Motion and Free Fall Motion_NOTES.pptxALVINMARCDANCEL2
An object is in Free-Fall when the only force acting on the object is the Force of Gravity, however, we haven’t defined
Force much less the Force of Gravity, so, until we have defined the Force of Gravity, we have a slightly different definition.
An object is in Free-Fall when:
- It is not touching any other objects♥
- There is no air resistance (it’s in the vacuum we can breathe)
We are now in the vacuum that we can breathe and will be for the remainder of this class, unless otherwise stated.
Common Misconception: For some reason people think the word “fall” in Free-Fall means that the object must be going
down. This is absolutely, not true. An object thrown upward is in Free-Fall from the moment it leaves the persons hand
until it touches the ground.
This ppt was created by Dr Beka a lecture from Ekwendeni College of Health Sciences (ECoHS) Ekwendeni Mzimba Malawi. It is understandable and easy to read for students who are studying clinical medicine
Ph2A Win 2020 Numerical Analysis Lab
Max Yuen
Mar 2020
(use g = 9.8m/s2 for all problems.)
Background
Many physics problems cannot be solved directly by hand or analytically. We resort to numerical
methods to give us approximations to the problem. In this lab you will learn the Euler method,
which allows you to solve Newton’s laws of motion. This is done by treating the velocity as a
piecewise linear function with many time intervals and during interval the acceleration is assumed
to be uniform. This allows us to use the kinematic equations we learned about in the first half
of the class to approximate the motion. If we choose to partition the motion into smaller time
intervals, the approximation becomes much better since the differences between adjacent intervals
become smaller. In this lab, this numerical analysis method will be applied to the motion of a
falling object under the influence of gravity and drag force. If you are adventurous, you can even
try to extend this to 2D and compute the realistic trajectory of a baseball. You might even try
some other problems, such as a mass attached to a spring.
Euler’s Method Foundations
This method is well suited for problems where the acceleration is a function of the velocity, as in
the case of a falling object under the influence of gravity and drag:
a = f(v) (1)
Falling object with drag force
The model for drag fits the prescription for using Euler’s method since the net force on a falling
object with drag is given by:
ma = −mg −FD (2)
ma = −mg −
1
2
ρairACDv
2 · sgn(v) (3)
a = −g
(
1 +
ρairACDv
2 · sgn(v)
2mg
)
(4)
a = f(v) ← Equation of Motion (5)
where m is the mass of the falling object, a is the acceleration of the object (which is positive when
pointed up), ρair is the density of air (about 1.29 ·10−3kg/m3), A is the cross-sectional area, CD is
the drag coefficient, v is the object’s velocity, and sgn(v) is the signum function which returns the
sign of the argument. The second signum function is there to guarantee that the direction of the
drag force is always in the opposite direction of the velocity function. Note that we see that the
acceleration is an explicit function of v, which sort of makes this a chicken or egg problem. This is
because we need a to get v, but to get a we need v, so which one do we compute first? Hold that
thought. We’ll talk more on how to program this in EXCEL or Google Sheets later.
1
Figure 1: FBD for an object falling under the pull of gravity and resistance by drag force
Terminal Velocity
In lecture, we talked about how after waiting for some time, if the object started at rest the
speed will increase and the drag force will also become larger and eventually balance out with the
gravitational force. When this happens, we have reached terminal velocity vterm = −v. This can
be solved by setting a = 0:
0 = −mg −
1
2
ρairACDv
2 · sgn(v) (6)
2mg = ρairACDv
2
term (7)
→ vterm =
√
2mg
ρairACD
(8)
Using this definition for the terminal ...
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
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We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
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Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
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It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
2. Additionalskillsgained:
• Advancedcalculation
• ComponentIsolation
Objectives:
• Spec point 9: be able to use the equations for uniformly
accelerated motion in one dimension using SUVAT equations
• Spec point 15: understand how to make use of the
independence of vertical and horizontal motion of a projectile
moving freely under gravity
3. Lesson-Link: The string of beads…
https://www.youtube.com/watc
h?v=nDKGHGdXLEg
You have 10mins to
figure it out….
6. From simple…
What is the simplest equation you can
think of that relates distance, speed
and time?
Convert this into a vector form
You use this equation when there is
NO ACCELERATION
OCCURRING!
s =
𝒅
𝒕
v =
𝒔
𝒕
Careful! Displacement
is shown by an ‘s’ but
it’s not representing
speed!
7. To complex…
So far, we have covered equations for constant motion but
without acceleration. So how do we deal with motion with
constant acceleration?....
SUVAT
It’s an acronym! Write the word nice and big and using colours!
For each one, annotate what it represents and the unit it is
measured in!
8. Unravelling the maths…
Don’t forget as we’re going through this that these equations
only work with constant acceleration and that often the value
for acceleration can be substituted for ‘g’ as gravitational force
is commonly used in questions!
SUVAT
Task: We are soon going to start a flow chart of the equations!
Start these on a new page with clear highlighting of the
equations.
9. Step 1, equation 1 SUVAT
Rearrange the equation for acceleration to have v as the
subject
𝒂 =
𝒗 − 𝒖
𝒕
𝒗 = 𝒖 + 𝒂𝒕
10. Step 2, equation 2 SUVAT
If acceleration is constant then what is the average velocity of a
journey between two points?
𝒖 𝒗
𝒖 + 𝒗
𝟐
a.k.a
Average ‘v’
Try combining this with the equation
for non-acceleration displacement
(s= v x t)
s = (
𝒖+𝒗
𝟐
) × 𝒕
11. 1 + 2 makes equation 3!
SUVAT
We need to combine the first and second equations. Let’s try
first to do it by putting the first into the second…
Work out the simplest form…
s = (
𝒖+𝒗
𝟐
) × 𝒕
𝒗 = 𝒖 + 𝒂𝒕
13. 1 + 2 makes equation
4…as well…
SUVAT
If we combine the equations again but this time changing
equation 1 to be in the form of t….
s = (
𝒖+𝒗
𝟐
) × 𝒕
𝒗 = 𝒖 + 𝒂𝒕
𝒕 =
𝒗 − 𝒖
𝒂
s = (
𝒖+𝒗
𝟐
) ×
(𝒗−𝒖)
𝒂
2as = 𝒖 + 𝒗 × (𝒗 − 𝒖)
2as = 𝒖𝒗 + 𝒗𝟐 − 𝒖𝟐 − 𝒗𝒖
v2 = 𝒖𝟐 + 𝟐𝒂𝒔
14. What we haven’t got… SUVAT
Make a table whereby you have all of the equations on the left
hand side, and the quantity that is missing each time. If the
SUVAT doesn’t contain the needed variable then don’t use it!
𝒗 = 𝒖 + 𝒂𝒕
s = (
𝒖+𝒗
𝟐
) × 𝒕
𝐬 = 𝐮𝐭 +
𝟏
𝟐
𝐚𝐭𝟐
v2 = 𝒖𝟐 + 𝟐𝒂𝒔
15. Worked
Example
A man drops a rock from the top of a cliff and the rock
takes 3 second to reach the bottom. Calculate both the
velocity it reaches before hitting the ground and the
distance it fell
1. Pick the Equation:
• Which equation contains the quantity we want and a quantity we know?
• Only two equations have both, and
• We can’t use the first one as it contains ‘s’ which we do not know yet! So we
use the second!
We want: v
We have: t
𝐬 = 𝐮𝐭 +
𝟏
𝟐
𝐚𝐭𝟐 𝒗 = 𝒖 + 𝒂𝒕
2. Rearrange:
• Rearrange the equation to make the needed quantity the subject. Luckily in
this case we don’t need to!
3. Plug the values in:
• We know that time here is 3s, we know that the initial velocity was 0m/s and
acceleration must be 9.81 m/s2.
𝒗 = 𝒖 + 𝒂𝒕 𝒗 = 𝟎 + (𝟗. 𝟖𝟏 × 𝟑) 𝒗 = 𝟐𝟗. 𝟒 m/s1
16. Worked
Example
A man drops a rock from the top of a cliff and the rock
takes 3 second to reach the bottom. Calculate both the
velocity it reaches before hitting the ground and the
distance it fell
4. Repeat for the other quantity:
• Which equation contains the quantity we want and a quantity we know?
• Two equations can be used here: and
• So s = 0 m/s*3s + ½ *9,81 m/s2 * (3 s)2 s = 44.1 m
• Solving for ‘s’ gives us 44.1 m!
We want: s
We have: t (3 s) and v (29.4 m/s)
𝐬 = 𝐮𝐭 +
𝟏
𝟐
𝐚𝐭𝟐 v2 = 𝒖𝟐 + 𝟐𝒂𝒔
The key to SUVAT calculations is just to spend a little
time working out the correct equation to use!
17. Practice Questions
A bird drops a stone
from 88m above a
pond, how long will it
take the stone to hit
the surface and what
speed will it be
travelling at just before
it hits the water?
An alien is holidaying
on Pluto and throws a
tennis ball vertically
upward at a speed of
20ms-1 causing it to
reach the peak of its
journey a whopping
303m above the point
of release. Calculate the
acceleration due to
gravity on Pluto
19. Additionalskillsgained:
• Advancedcalculation
• ComponentIsolation
Objectives:
• Spec point 9: be able to use the equations for uniformly
accelerated motion in one dimension using SUVAT equations
• Spec point 15: understand how to make use of the
independence of vertical and horizontal motion of a projectile
moving freely under gravity
Editor's Notes
Force for one = cos 35 x 6500 = 5324. Both = 10648N. A= F/m = 10.6ms-2
