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2.1. Motion

For GCSE we were happy with using the equation 'speed = distance/ time' - an equation that is very useful when we talk about movement at a CONSTANT SPEED. However, if something is  accelerating, that equation is less useful. Now, at IB we want to start thinking about movement with CONSTANT ACCELERATION. For this, we have a set of equations you probably know as the SUVAT equations.

This CrashCourse video is a nice starting point for this section, take a look.

The section has been broken up as follows: 

 

 

Equations of Motion

To start off with, we need to make sure we are confident with the various concepts of displacement, velocity and acceleration (and their scalar equivalents). If you need a bit of a recap, flick back to the previous section on vectors (particularly resolving, addition and subtraction). 

It's also useful to now start thinking about velocity as the rate of change of displacement. This draws upon an area of mathematics called calculus -a.k.a. differentiation and integration (hopefully you are familiar already with these ideas from Maths class). Velocity is the derivative of displacement with respect to time (i.e. v = ds / dt). Acceleration is the second derivative of displacement (i.e. a = d²s / dt²).  Although you won't need to differentiate or integrate any equations for the IB, understanding the basics of calculus and how they link to graphs is important.

Crash course have a couple of nice videos here which draw together the Physics and Maths.

We have a number of equations that fall out of our definitions. It is important that we are familiar with these basics.

  • Velocity is the rate of change of displacement. As an equation this gives us velocity = displacement / time.

  • Acceleration is the rate of change of velocity. As an equation this gives us acceleration = velocity / time.

 

 Displacement, velocity and acceleration are all vector quantities. This means that direction must be considered, and that they obey the rules of vector geometry (e.g. we can add multiple velocity vectors to give a resultant velocity).

You should also understand the scalar equivalents, distance and speed - in these cases the direction is irrelevant, (so these values can not be negative).

As a bit of a fun follow up - I quite enjoy this video by Tom Scott, discussing acceleration (2nd derivative of displacement) and jerk (3rd derivative) - as well as less commonly used 4th, 5th and 6th derivatives called snap, crackle and pop respectively.

Video Lessons

Resources

IB Physics
Topic 2 Notes
IB-Physics.net
Chapter 2 Summary
IB Revision Notes
Isaac Physics
Equations of Motion
Isaac Physics
Equations of Motion
Mr. G
2.1 Teaching Notes
2.1 Student Notes
Physics and Maths Tutor
Motion Definitions
Motion Key Notes
Motion Detailed Notes
Mechanics Flashcards
A Level Resources - content slightly different

Questions

Cambridge University Press
Topic 2: Add Qs
Topic 2: Add Qs MS
Topic 2: MCQs
CUP Website Link
Freely available online
Dr French's Eclecticon
Kinematics
Kinematics Solutions
Link to Dr French's Site
Extension: Pre-University Material
Grade Gorilla
2.1 (Motion Graphs) MCQs
Topic 2 (Mechanics A) Final Quiz
Quick IB Specific Mixed MCQs
Mr. G
2.1 Formative Assessment
Topic 2 Summary Qs
IB Specific Questions
Physics and Maths Tutor
Equations & Graphs of Motion (Edexcel 1)
Equations & Graphs of Motion MS (Edexcel 1)
Motion (OCR)
Motion MS (OCR)
A-Level Qs: overlapping content
Physics and Maths Tutor
Motion & Force (AQA 1)
Motion & Force MS (AQA 1)
Mechanics (Edexcel 2)
Mechanics MS (Edexcel 2)
A-Level Qs: overlapping content
 

Motion Graphs

Graphical representation of motion is particularly useful. Again, you were probably introduced to these at GCSE, but we dive much deeper into this in the IB. You will need to be completely confident with how to interpret both displacement/ time graphs and velocity/ time graphs.

 

We have already seen that velocity is the derivative of displacement. This means that, we can find the velocity at any point on a displacement/ time graph by finding the gradient (differentiation) at that point. Conversely, you can find the total displacement at any point on a velocity/ time graph by finding the area between the graph and x-axis (integration). Once you've got to grips with these, have a go at getting your head around acceleration/ time graphs.

The below example shows displacement/ time  and velocity/ time graphs for an object travelling at constant velocity.

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PHET have two nice simulations that help with this. 

1) Calculus Grapher (requires Flash, so try Edge rather than Chrome)

- Ensure integral and derivative are ticked. Now the top graph illustrates displacement, the middle velocity and the bottom acceleration. Try out different shapes and work out how the others change.

2) The Moving Man

- The 'Charts' tab is most useful. Move the man at a constant speed/ accelerating and compare displacement, velocity and acceleration.

Take a look at this video by PhysicsOnline. It explains nicely a few of the key points, and allows these graphs to be visualised side by side.

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Finally, have a go on this applet by Geogebra. Try changing the velocity and making a prediction about the effect on the displacement and acceleration graphs.

Worked Example - a ball being thrown into the air

Here let's take a look at what these graphs look like with a (seemingly) fairly straight-forward example, a ball being thrown in the air and caught at the same height.

  • Let's start with our displacement/ time graph. The ball follows a parabolic path during its flight. The displacement at the start and end is zero in each case (as it starts and ends at the same height). A tangent has been drawn in yellow at a couple of points to allow us to calculate our velocity. 

  • Our velocity/ time graph is the derivative of our displacement/ time. That means if we calculate the gradient at each point, that will give us our velocity at each time. The ball is moving upwards fastest the instant it is released. Straight away it begins slowing down due to gravity (at a constant rate). At the top of its path it has a velocity of zero, the point at which our velocity/ time crosses the x- axis. It then starts accelerating downwards, with an increasing negative velocity.

  • Our acceleration/ time graph is the derivative of our velocity time. As our velocity/ time graph is a straight line, our acceleration will be constant throughout. As our velocity/ time has a negative gradient, the acceleration will have a negative value. The exact value of this acceleration would be -9.81 msˉ², or 'g'.

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Video Lessons

Resources

Questions

 

SUVAT Equations

SUVAT equations are a set of 5 equations that describe the motion of something moving with a constant acceleration. SUVAT comes from the variables used to describe motion s - displacement (m), u - initial velocity (msˉ¹), v - final velocity (msˉ¹), a - acceleration (msˉ²) and t - time (s). 

The derivation of the 5 equations are neatly summarised by PhysicsOnline:

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Each of the 5 equations (though only 4 are normally used) consist of 4 out of the 5 suvat variables, with one missing. A typical question will involve you being given 3 of these values (e.g. displacement travelled, initial velocity and time) and asked to work out a 4th (e.g. acceleration). 

It is important that we structure our working properly. Always start by writing your suvat variables out, before choosing which equation to use. 

i) Write out the letters suvat vertically down the page. Using the information given in the question, fill in these variables.

ii) Look at which 4 variables you are interested in, and use this to decide on which equation you need - use your formula book to help, these equations are given to you!

iii) Substitute and solve!

Worked Example - an acceleration car

Take a look at this as a typical example:

A car accelerates from 10 msˉ¹ at a rate of 2 msˉ². At what velocity will the car be travelling after it has travelled 100m?

Step i) Write out your suvat variables:

s = 100 m

u = 10 msˉ¹

v = ? msˉ¹

a = 2 msˉ²

t = x

N.B. I've put a question mark for the variable I am trying to find, and a cross for the variable I am not interested in.

Step ii) Choose your equation

I need an equation that contains the variables s, u, v and a, without t. From my formula book I can see that the equation I need is:

           v² = u² + 2as 

Step iii) Substitute and solve

v² = 10² + 2 x 2 x 100

     = 500

v =  √500 = 22 msˉ¹

PhysicsOnline has a nice video working through how to solve SUVAT problems. Once you've watched that, have a go at looking through Isaac Physics' lesson on SUVAT and practice questions.

Now have a bit of practice on this using this applet by Geogebra. You can change the initial velocity and starting height and see how it's velocity changes over time. Try the following:

i) Projecting downwards and calculating the speed at which it hits the ground.

ii) Projecting downwards and calculating the time at which it hits the ground.

iii) Projecting upwards and calculating the time at which it reaches its max height.

iv) Projecting upwards and calculating the max height reached.

v) Projecting upwards and calculating the speed at which it hits the ground.

vi) Projecting upwards and finding the total time before it hits the ground (Hint: It is sometimes easier to split into 2 parts- 'travelling up' and 'travelling down').

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Required Practical - finding a value for g by freefall

There are a few required practical experiments that you should complete as part of your Physics IB course. The exact method is left fairly open for teachers to be able to adapt for their own classes so they will vary slightly from classroom to classroom, but the overall aim should be the same. It is important that you are familiar with each of the required practicals as they may be looked at in the practical section of your Paper 3 paper.

The first is to find a value for gravity using a freefall method. The simplest method is to drop a ball and time how long it takes to hit the ground, then using SUVAT to obtain a value for g. The below video talks through a few of the key ideas involved in this investigation.

Video Lessons

Resources

IB Physics
Topic 2 Notes
IB-Physics.net
Chapter 2 Summary
IB Revision Notes
Mr. G
2.1 Teaching Notes
2.1 Student Notes
Physics and Maths Tutor
Motion Definitions
Motion Key Notes
Motion Detailed Notes
Mechanics Flashcards
A Level Resources - content slightly different

Questions

Cambridge University Press
Topic 2: Add Qs
Topic 2: Add Qs MS
Topic 2: MCQs
CUP Website Link
Freely available online
Grade Gorilla
2.1 (SUVAT) MCQ
Topic 2 (Mechanics A) Final Quiz
Quick IB Specific Mixed MCQs
Isaac Physics
Uniform acceleration
Mr. G
2.1 Formative Assessment
Topic 2 Summary Qs
IB Specific Questions
Physics and Maths Tutor
Linear Motion (AQA 2)
Linear Motion MS (AQA 2)
Motion (OCR)
Motion MS (OCR)
A-Level Qs: overlapping content
Physics and Maths Tutor
Motion & Force (AQA 1)
Motion & Force MS (AQA 1)
Mechanics (Edexcel 2)
Mechanics MS (Edexcel 2)
A-Level Qs: overlapping content
 

Projectile Motion

Once you are completely confident with your SUVAT and have had some practice at calculating things like time of flight and maximum height reached, we can start looking at motion in two dimensions, i.e. projectiles. 

There are plenty of classic examples used when discussing projectiles, including tennis balls, bullets and cannonballs. Imagine a tennis ball hit horizontally - it will follow a parabolic path as it accelerates downwards due to gravity.

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The key thing we need to understand to fully get to grips with projectiles is that because velocity is a vector, we can are able to split this into the vertical and horizontal directions (i.e. resolve my velocity vector, v, into its x- and y-components, vx and vy). In the vertical direction the object will accelerate solely under the influence of gravity (the horizontal movement has no impact on this). In the horizontal direction, the object will travel at a constant speed (in the absence of air resistance - a normal assumption we make).

CrashCourse Physics explains the Vector mathematics in the video below:

When solving projectile problems we must separate our x- and y-components. In the y-direction we use suvat under the influence of gravity; in the x-direction we use speed = distance/ time. To ensure I completely separate these in my mind, I always physically divide my paper in half (definitely don't short cut your working when solving these problems!):

y-direction (vertical)

In the vertical direction, the object is accelerating under gravity, therefore we use our suvat equations.

sy = 

uy =

vy =

ay = g (or -g) 

t = time of flight

x-direction (horizontal)

In the horizontal direction, the object is travelling at a constant speed, therefore we can use velocity = displacement/ time

sx = 

ux =

t = time of flight 

When laying out these problems, there are a few things to watch out for.

  • One of the main areas for confusion come in setting out your variables. You need to pick a direction as positive (typically upwards), which means that any velocities/ accelerations/ displacements downwards will be negative.

  • You may also need to split a diagonal vector (e.g. if a cannonball is fired at 45° to the horizontal) into its horizontal and vertical components (see resolving vectors).

  • As with some of your suvat problems, it often makes sense to split the trajectory of the ball into two parts ('travelling up' and 'travelling down') - make sure you draw a diagram to keep things really clear.

Take a look at these two videos by Physics Online, which explain how to tackle projectiles problems of different types and how to structure your work properly.

For a bit of practice take a look at these Geogebra simulations (basic simulation and full simulation). Experiment by changing the launch speed and angle, and trying to predict the maximum height reached and the horizontal range in each case.

Video Lessons

Resources

IB Physics
Topic 2 Notes
IB-Physics.net
Chapter 2 Summary
IB Revision Notes
Mr. G
2.1 Teaching Notes
2.1 Student Notes
Physics and Maths Tutor
Motion Definitions
Motion Key Notes
Motion Detailed Notes
Mechanics Flashcards
A Level Resources - content slightly different

Questions

Cambridge University Press
Topic 2: Add Qs
Topic 2: Add Qs MS
Topic 2: MCQs
CUP Website Link
Freely available online
Dr French's Eclecticon
Projectiles
Projectiles Solutions
Link to Dr French's Site
Extension: Pre-University Material
Grade Gorilla
2.1 (SUVAT) MCQ
Topic 2 (Mechanics A) Final Quiz
Quick IB Specific Mixed MCQs
Isaac Physics
Trajectories
Mr. G
2.1 Formative Assessment
Topic 2 Summary Qs
IB Specific Questions
Physics and Maths Tutor
Projectiles (AQA 2)
Projectiles MS (AQA 2)
Motion & Projectiles (AQA 1)
Motion & Projectiles MS (AQA 1)
A-Level Qs: overlapping content
Physics and Maths Tutor
Motion & Force (AQA 1)
Motion & Force MS (AQA 1)
Mechanics (Edexcel 2)
Mechanics MS (Edexcel 2)
A-Level Qs: overlapping content
 

Additional Resources

IBPhysics.org have collated some nice resources on this topic.

Physics and Maths Tutor have a good set of detailed (A Level) notes on the topic, relevant pages are 1-9. Ignore the stuff on Materials, not on the IB. Nor are moments a big part of the IB.

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Definitions and Key Words : Chapter 2

A set of Quizlet flashcards of the key words and definitions for this chapter is provided here. 

A question by question breakdown of the IB papers by year is shown below to allow you to filter questions by topic. Hopefully you have access to many of these papers through your school. If available, there may be some links to online sources of questions, though please be patient if the links are broken! (DrR: If you do find some broken links, please contact me through the site)

 

Questions on this topic (Section 2) are shown in red.