YOU ARE LEARNING:
The Formula for Acceleration
The Formula for Acceleration
You find acceleration by dividing the change in velocity by time.
An example
How fast is this cyclist going?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/GIhG7PwARSeBRf8hRlvY.png)
10 seconds later, how fast is the cyclist going?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/3pqBc8qGT91RbLECl8SS.png)
How much faster is 10 m/s than 5 m/s?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/3pqBc8qGT91RbLECl8SS.png)
So over the course of 10 s, this cyclist got 5 m/s faster. How many m/s did the cyclist get faster every second?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/3pqBc8qGT91RbLECl8SS.png)
So every second, this cyclist accelerated by 0.5 m/s
You say that his acceleration was 0.5 m/s2
The unit m/s2 will be explained a little later in this lesson.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/eJef0iXbSACKbl1HRFni.png)
You worked out the cyclist's acceleration like this 10 s10 m/s−5 m/s=0.5 m/s2. So what is the correct formula for acceleration?
The unit m/s2 explained
This is the formula for acceleration. What is the unit you have used for speed in this lesson?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/yMh9PmCcSM9doXpY8Os6.png)
What is the unit you have used for time in this lesson?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/yMh9PmCcSM9doXpY8Os6.png)
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
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/doLihjv2SdCUM6iabHIt.png)
sm/s is the same as s×sm. How can you also write s×s, using powers?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/doLihjv2SdCUM6iabHIt.png)
sm/s is the same as s×sm which is the same as s2m
That is why the unit for acceleration is m/s2 and not simply m/s (which is the unit for speed!).
Acceleration is a change in metres per second per second.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/gMSOR0yvQMaSTEA248Xt.png)
What is this woman's acceleration in m/s2?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/xz3Jb6IdRJeX4PENkhsb.png)
What is this cyclist's acceleration in m/s2?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/TaHwsFPRQipEIEkHE5eh.png)
Careful now!
What is this cyclist's initial speed?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/wunQjecRQiS1ZXVpSQ5W.png)
What is his final speed?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/wunQjecRQiS1ZXVpSQ5W.png)
Is this cyclist speeding up or slowing down?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/wunQjecRQiS1ZXVpSQ5W.png)
Use the formula acceleration=timefinal speed−initial speed as normal. What is the cyclist's acceleration?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/wunQjecRQiS1ZXVpSQ5W.png)
So acceleration can be negative!
If an object is slowing down, it's still "accelerating", but the acceleration is negative.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/hMm6eUSGQFy4lO2XU3jp.png)
Summary!
You calculate acceleration like this
acceleration=timefinal speed−initial speed
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/eJef0iXbSACKbl1HRFni.png)
This gives you the unit m/s2
You essentially say sm/s which is the same as s×sm or s2m
Acceleration is a change in metres per second per second.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/gMSOR0yvQMaSTEA248Xt.png)
If an object is slowing down it is still "acceleration"
It just means that acceleration will be negative because final speed−initial speed will give a negative value.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/hMm6eUSGQFy4lO2XU3jp.png)