Albert Teen YOU ARE LEARNING:  The Formula for Acceleration  # The Formula for Acceleration ### The Formula for Acceleration

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

An example

1

How fast is this cyclist going?  2

10 seconds later, how fast is the cyclist going?  3

How much faster is $10 \space m/s$ than $5 \space m/s$?  4

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

So every second, this cyclist accelerated by $0.5 \space m/s$

You say that his acceleration was $0.5 \space m/s^2$

The unit $m/s^2$ will be explained a little later in this lesson. You worked out the cyclist's acceleration like this $\frac{10 \space m/s - 5 \space m/s}{10 \space s}=0.5 \space m/s^2$. So what is the correct formula for acceleration? The unit $m/s^2$ explained

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This is the formula for acceleration. What is the unit you have used for speed in this lesson?  2

What is the unit you have used for time in this lesson?  3

The image now also shows the formula in units

It shows that acceleration is a change in meters per second per second, because $m/s$ is divided by $s$ 4

$\frac{m/s}{s}$ is the same as $\frac{m}{s \times s}$. How can you also write $s \times s$, using powers?  5

$\frac{m/s}{s}$ is the same as $\frac{m}{s \times s}$ which is the same as $\frac{m}{s^2}$

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

Acceleration is a change in metres per second per second. 1

What is this woman's acceleration in $m/s^2$?  1

What is this cyclist's acceleration in $m/s^2$?  Careful now!

1

What is this cyclist's initial speed?  2

What is his final speed?  3

Is this cyclist speeding up or slowing down?  4

Use the formula $acceleration = \frac{final \space speed - initial \space speed}{time}$ as normal. What is the cyclist's acceleration?  5

So acceleration can be negative!

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

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You calculate acceleration like this

$acceleration = \frac{final \space speed - initial \space speed}{time}$ 2

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

You essentially say $\frac{m/s}{s}$ which is the same as $\frac{m}{s \times s}$ or $\frac{m}{s^2}$

Acceleration is a change in metres per second per second. 3

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

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