CCEA GCSE Physics

## Average speed Speed says how quickly an object covers distance. Distance is measured in metres (m), time in seconds (s) and speed in metres per second (m/s). Over a whole trip the speed usually changes, so what is calculated is the **average speed**: $$\text{average speed} = \frac{\text{distance moved}}{\text{time taken}}$$ A cyclist who covers 1 800 m in 300 s has an average speed of $1800 \div 300 = 6.0$ m/s. If an object speeds up or slows down at a steady rate, its average speed can also be found from the speeds at the start and the end of the motion: $$\text{average speed} = \frac{\text{initial speed} + \text{final speed}}{2}$$ A train slows steadily from 30 m/s to 10 m/s. Its average speed is $(30 + 10) \div 2 = 20$ m/s, so in 50 s it moves $20 \times 50 = 1000$ m. The equation only works when the change of speed is steady, because it treats the speed as sitting halfway between the two values. ## Rate of change of speed The rate of change of speed says how quickly the speed is going up or down. It is measured in metres per second squared (m/s²), because it is a change of speed in m/s divided by a time in s. $$\text{rate of change of speed} = \frac{\text{final speed} - \text{initial speed}}{\text{time taken}}$$ A car moves off from rest and reaches 24 m/s after 8.0 s. $$ \begin{aligned} \text{rate of change of speed} &= \frac{24 - 0}{8.0} \\ &= 3.0\ \mathrm{m/s^2} \end{aligned} $$ This means its speed rises by 3.0 m/s in every second. A negative answer means the…