# Acceleration

Acceleration is defined as follows:

$acceleration= \frac{\Delta v}{time taken}$

$$\Delta v$$ (pronounced 'delta v' is the change in speed of the object.

Acceleration is measured in metres per second per second or metres per second squared $$m\, s^{-2}$$.

### Example

Question

A sprinter starting at $$0\,m\, s^{-1}$$ in the blocks, reaches a speed of $$10\, m\, s^{-1}$$ in 4 seconds. Calculate the acceleration.

$a=\frac{\Delta v}{t}$

$= \frac{10}{4}$

$=2.5\, m\, s^{-2}$

We sometimes refer to a moving object as having a 'constant acceleration' or a 'uniform acceleration'. A constant or uniform acceleration means that the speed of the object changes by the same amount every second.

Acceleration and force

If an object is slowing down, when the acceleration is calculated, the answer is negative.

### Example

Question

A cyclist approaching a traffic light slows down from $$5\, m\, s^{-1}$$ to $$0\, m\,s^{-1}$$ in 10 seconds. Calculate the acceleration.

$a=\frac{\Delta v}{t}$

$=\frac{-5}{10}$

$= 0.5\, m\, s^{-2}$

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