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.
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This CrashCourse video is a nice starting point for this section, take a look.
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The section has been broken up as follows:

Equations of Motion  What are Displacement, Velocity and Acceleration?

Motion Graphs  How can we graphically represent motion?

SUVAT Equations  Making use of the equations of constant acceleration

Projectile Motion  Motion in 2 dimensions
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).
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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.
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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
Chris Doner  Kinematic Concepts  Acceleration  IB Specific  
Khan Academy  Calculating Average Speed  Solving for Time  Displacement  Instantaneous Speed  
Khan Academy  Kinematics Playlist  
Khan Academy  Acceleration  Airbus Example  Airbus Example 2  
Physics Online  Speed, Velocity & Acceleration  Displacement vs Distance  
Study Nova  Uniformly Accelerated Motion  Equations of Motion (Lecture) 
Resources
IB Physics  Topic 2 Notes  
IBPhysics.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: PreUniversity 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  Motion & Force (AQA 1)  Motion & Force MS (AQA 1)  Mechanics (Edexcel 2)  Mechanics MS (Edexcel 2)  ALevel Qs: overlapping content  
Physics and Maths Tutor  Equations & Graphs of Motion (Edexcel 1)  Equations & Graphs of Motion MS (Edexcel 1)  Motion (OCR)  Motion MS (OCR)  ALevel 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 xaxis (integration). Once you've got to grips with these, have a go at getting your head around acceleration/ time graphs.
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The below example shows displacement/ time and velocity/ time graphs for an object travelling at constant velocity.
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.
 The 'Charts' tab is most useful. Move the man at a constant speed/ accelerating and compare displacement, velocity and acceleration.
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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.
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 straightforward example, a ball being thrown in the air and caught at the same height.
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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 msË‰², or 'g'.
Video Lessons
Chris Doner  Position Time Graphs  Position Time Graphs ii  Velocity Time Graphs  IB Specific  
Khan Academy  Position Time Graphs  Area under velocity time  Acceleration Time Graphs  Playlist : 816  
Khan Academy  Motion Graphs Playlist  
Physics Online  Distance & Speed Time  Displacement & Velocity Time  Tricky Points  
Study Nova  Graphing Accelerating Motion  Graphing Motion (Lecture)  Graphing Motion (Lecture 2)  
Study Nova  Graphing Motion 
Resources
IB Physics  Topic 2 Notes  
IBPhysics.net  Chapter 2 Summary  IB Revision Notes  
Isaac Physics  Displacement, Velocity and Acceleration  
Mr. G  2.1 Teaching Notes  2.1 Student Notes  
Physics Classroom  Basics  Position Time Graphs  Velocity Time Graphs  
Physics Classroom  Position Time Graphs  Velocity Time Graphs  Calculating Gradient  
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 (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)  ALevel Qs: overlapping content  
Physics and Maths Tutor  Motion & Force (AQA 1)  Motion & Force MS (AQA 1)  Mechanics (Edexcel 2)  Mechanics MS (Edexcel 2)  ALevel Qs: overlapping content 
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 (msË‰¹), v  final velocity (msË‰¹), a  acceleration (msË‰²) and t  time (s).
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The derivation of the 5 equations are neatly summarised by PhysicsOnline:
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).
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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 msË‰¹ at a rate of 2 msË‰². At what velocity will the car be travelling after it has travelled 100m?
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Step i) Write out your suvat variables:
s = 100 m
u = 10 msË‰¹
v = ? msË‰¹
a = 2 msË‰²
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.
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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
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Step iii) Substitute and solve
v² = 10² + 2 x 2 x 100
= 500
v = √500 = 22 msË‰¹
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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').
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.
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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  
IBPhysics.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)  ALevel Qs: overlapping content  
Physics and Maths Tutor  Motion & Force (AQA 1)  Motion & Force MS (AQA 1)  Mechanics (Edexcel 2)  Mechanics MS (Edexcel 2)  ALevel 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.
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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 ycomponents, 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:
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When solving projectile problems we must separate our x and ycomponents. In the ydirection we use suvat under the influence of gravity; in the xdirection 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!):
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ydirection (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
xdirection (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.
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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
Chris Doner  Projectiles I  Projectiles II  IB Specific  
Khan Academy  Horizontal Projectiles  Projectiles at an angle  Landing at different heights  Projectile Graphs  
Khan Academy  Max Projectile Range  Projectile Height  Plotting Projectiles  Further Projectiles Playlist  
Physics Online  Projectiles I  Projectiles II  
Science Shorts  Projectile Motion and Suvat  
Study Nova  Projectiles  Motion in 2D  
Study Nova  Motion in 2D 
Resources
IB Physics  Topic 2 Notes  
IBPhysics.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: PreUniversity 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  Motion & Force (AQA 1)  Motion & Force MS (AQA 1)  Mechanics (Edexcel 2)  Mechanics MS (Edexcel 2)  ALevel Qs: overlapping content  
Physics and Maths Tutor  Projectiles (AQA 2)  Projectiles MS (AQA 2)  Motion & Projectiles (AQA 1)  Motion & Projectiles MS (AQA 1)  ALevel Qs: overlapping content 
Additional Resources
IBPhysics.org have collated some nice resources on this topic.
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Physics and Maths Tutor have a good set of detailed (A Level) notes on the topic, relevant pages are 19. Ignore the stuff on Materials, not on the IB. Nor are moments a big part of the IB.
Definitions and Key Words : Chapter 2
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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.