Average speed can be calculated from the distance travelled and the time taken. The gradient of a distance-time graph is equal to the speed. Relative motion takes into account speed and direction.

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If you have travelled in a car on the motorway, you may have noticed that other cars passing by appear to move slowly past you, even though you know the actual speeds of the two cars are very high. This is because of their relative motion to each other.

The table summarises the different situations and how you can calculate the relative speed of two objects:

Situation | Relative speed |
---|---|

Objects moving in the same direction towards, or away from, each other | Fastest speed – slowest speed |

Objects moving in opposite directions towards, or away from, each other | Add the two speeds together |

- Question
Two cars are travelling in the same direction on a road. The blue car is travelling at 25 m/s in front of the red car, which is travelling at 30 m/s. What is their relative speed?

relative speed = 30 – 25 = 5 m/s

The red car is catching up with the blue car.

- Question
A railway line and a road are side by side. A train and a car are travelling in the same direction, with the train in front of the car. The train travels at 52 m/s and the car at 30 m/s. What is their relative speed?

relative speed = 52 – 30 = 22 m/s

The train moves further away from the car.

- Question
Two cars are travelling on a road in opposite directions. The blue car is travelling at 25 m/s and the red car is travelling at 30 m/s. What is their relative speed?

relative speed = 30 + 25 = 55 m/s