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The Formula for Acceleration
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The Formula for Acceleration

lesson introduction

The Formula for Acceleration

You find acceleration by dividing the change in velocity by time.

An example

1

How fast is this cyclist going?

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2

10 seconds later, how fast is the cyclist going?

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3

How much faster is 10 m/s10 \space m/s than 5 m/s5 \space m/s?

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4

So over the course of 10 s10 \space s, this cyclist got 5 m/s5 \space m/s faster. How many m/sm/s did the cyclist get faster every second?

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5

So every second, this cyclist accelerated by 0.5 m/s0.5 \space m/s

You say that his acceleration was 0.5 m/s20.5 \space m/s^2

The unit m/s2m/s^2 will be explained a little later in this lesson.

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You worked out the cyclist's acceleration like this 10 m/s5 m/s10 s=0.5 m/s2\frac{10 \space m/s - 5 \space m/s}{10 \space s}=0.5 \space m/s^2. So what is the correct formula for acceleration?

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The unit m/s2m/s^2 explained

1

This is the formula for acceleration. What is the unit you have used for speed in this lesson?

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2

What is the unit you have used for time in this lesson?

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3

The image now also shows the formula in units

It shows that acceleration is a change in meters per second per second, because m/sm/s is divided by ss

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4

m/ss\frac{m/s}{s} is the same as ms×s\frac{m}{s \times s}. How can you also write s×ss \times s, using powers?

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5

m/ss\frac{m/s}{s} is the same as ms×s\frac{m}{s \times s} which is the same as ms2\frac{m}{s^2}

That is why the unit for acceleration is m/s2m/s^2 and not simply m/sm/s (which is the unit for speed!).

Acceleration is a change in metres per second per second.

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1

What is this woman's acceleration in m/s2m/s^2?

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1

What is this cyclist's acceleration in m/s2m/s^2?

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Careful now!

1

What is this cyclist's initial speed?

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2

What is his final speed?

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3

Is this cyclist speeding up or slowing down?

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4

Use the formula acceleration=final speedinitial speedtimeacceleration = \frac{final \space speed - initial \space speed}{time} as normal. What is the cyclist's acceleration?

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5

So acceleration can be negative!

If an object is slowing down, it's still "accelerating", but the acceleration is negative.

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Summary!

1

You calculate acceleration like this

acceleration=final speedinitial speedtimeacceleration = \frac{final \space speed - initial \space speed}{time}

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2

This gives you the unit m/s2m/s^2

You essentially say m/ss\frac{m/s}{s} which is the same as ms×s\frac{m}{s \times s} or ms2\frac{m}{s^2}

Acceleration is a change in metres per second per second.

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3

If an object is slowing down it is still "acceleration"

It just means that acceleration will be negative because final speedinitial speedfinal \space speed - initial \space speed will give a negative value.

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