# Introduction

In this activity you will:

- find out what is meant by acceleration;
- look at cases where an object has constant acceleration;
- find a formula for the velocity of an object in terms of its initial velocity, constant acceleration and time.

# What is acceleration?

Which of the objects appears to have constant speed?

The object you picked has acceleration of $$0$$ ms^{-2} over the period of time shown.

You will look at some more cases of objects with zero acceleration next.

Acceleration is the rate of change of velocity.

It can be measured in ms^{-2}.

Press the **Start** button.

One of the objects on the right has constant velocity over the period of the animation shown.

Its rate of change of velocity, or its acceleration, is $$0$$ ms^{-2} for the whole period.

Pick this object and **Submit**.

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# Direction is important

You should always be aware of which direction is positive and which is negative when working with displacement, velocity and acceleration in a straight line.

Acceleration, velocity and displacement are all vectors. Their direction is important and you need to pay close attention to it.

In the examples you'll see here, motion is along a horizontal straight line and so direction is either 'left' or 'right'.

Throughout this walkthrough 'right' will be positive and 'left' will be negative.

Press the **Start** button to see the three objects move with constant velocity, i.e. with acceleration of

$$0$$ ms^{-2}.

Notice that those with negative velocity move left and those with positive velocity move right.

You can use the **Start** button as many times as you like. When you are ready to move on **Finish**.

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# Constant acceleration

Look carefully at the motion of each object and use the velocity-time graph shown.

You need to choose the object for which the velocity increases in equal quantities over equal periods of time.

This object has constant acceleration.

You'll explore this more next.

Now you'll look at some objects that have non-zero acceleration.

Press 'Start' and watch the objects on the right move.

A graph of the velocity in terms of time is drawn for both of them.

You can see that both have increasing velocity.

Both reach a velocity of 45 ms^{-1} after 5 seconds.

Which object has velocity which increases at a constant rate over the time period?

Use the graphs to help you decide.

Tick your choice and **Submit**.

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# Measuring constant acceleration

Look at the velocity axis of the diagram carefully.

Counting squares might help you work out how much the velocity increases each second.

The object has a constant acceleration of $$8$$ m^{-2}.

The velocity time graph for the object you picked on the last screen is shown on the right.

It has constant acceleration.

The time for the blue point on the right is one second later than for the one on the left.

Use the buttons to move the pair of points left and right.

Compare the velocity at the point on the left to the velocity at the point on the right, one second later.

Answer the question and then **Submit**.

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# What's my velocity?

The object has velocity 2ms^{-1} at when t = 0.

Its velocity increases by 3ms^{-1} every second.

So what is its velocity after 1 second, after 2 seconds and after 4 seconds?

Next you'll think about a general formula for this.

Here you will think about how to calculate the velocity of an object moving with constant acceleration given that you know its initial velocity.

Press the **Start** button on the right.

The object shown has an initial velocity of 2 ms^{-1} and then accelerates at a constant rate of

3 ms^{-2}.

This means its velocity increases by 3 ms^{-1} every second.

Calculate the missing values on the vertical velocity axis of the graph.

When you've filled them in **Submit**.

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# A general formula

Does the formula you've chosen work for the example at the top of the page?

You needn't be working in units of metres and seconds for this to work.

As long as your units are consistent across $$u$$, $$v$$, $$a$$ and $$t$$ your calculation will be correct.

Here you will think about a general formula for the velocity of an object moving under constant acceleration, $$a$$ ms^{-2}.

It will depend on the initial velocity,

$$u$$ ms^{-1} of the object and the amount of time, $$t$$ s, it has been accelerating for.

Consider the example at the top and look at how the velocity is calculated at the end of each second.

Use the buttons to change the number of seconds considered.

Then try to pick out the correct general formula below.

Then **Submit**.

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# Slowing it down

You need to use the formula $$v=u+at$$ with $$u=20$$, $$a=-3$$ and $$t=4$$.

Next you'll see an example where the acceleration slows an object down to rest and then changes its direction.

For an object moving in a straight line, if its acceleration is in the opposite direction (has the opposite sign) to its velocity then it will slow down.

Here you see an example of an object with positive initial velocity and negative acceleration.

Use $$v=u+at$$ and the graph to work out its velocity after 6 seconds.

Input your answer on the velocity axis of the graph and **Submit** to check it.

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# Acceleration changing an object's direction

You need to set $$v=0$$ in the equation $$v=u+at$$ and solve for $$t$$.

The animation and graph can help too.

You can see that objects moving with constant acceleration can have very interesting movement.

The initial velocity of the object shown here is negative and it moves with a positive constant acceleration.

The object starts moving left but, over time, its positive acceleration slows it down and eventually changes its direction.

Press **Start** to see the object move.

Think about how you could use $$v=u+at$$ to work out the moment in time when it has zero velocity. At this instant in time it is not moving at all, it is about to change direction.

Add this to the time axis and **Submit** to check.

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# More useful examples

As you might imagine this mathematics has many real world applications to moving objects.

The objects on the right have a random initial velocity and a random constant acceleration.

Informally (your answers won't be checked!) try make predictions about how each of the objects will move.

Then press **Start** to see them move.

You can repeat this as many times as you like using the buttons, press **Finish** to move on.

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# Finally...

Youâ€™ve now completed this activity. Go and explore the other resources!

In this walkthrough you have learned:

- what it means for an object to move with constant acceleration;
- that, if an object has initial velocity $$u$$ ms
^{-1}and then moves with a constant acceleration of $$a$$ ms^{-2}for $$t$$ seconds then its velocity, $$v$$ms^{-1}, will then be $$v = u + at$$. - that acceleration can make objects move more slowly and even change their direction.