The motion of any moving object can be described by its speed– time graph. Data from the graph can be used to calculate acceleration, the distance travelled and the average speed for the motion.

**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 \(m\, s^{-2}\).

- 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.

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

- 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.

\[a=\frac{\Delta v}{t}\]

\[=\frac{-5}{10}\]

\[= 0.5\, m\, s^{-2}\]