Relative motion

In a nutshell

Sometimes, it is useful to know how fast an object is moving when you are moving too. This is harder to do than calculating the speed of an object if you are standing still, you need to take into account your own speed and whether the object is coming towards you or moving away from you.

​

Two objects moving in opposite directions

If there are two objects moving in opposite directions, they are moving towards each other. If the two objects are moving towards each other on the same straight line, then you can figure out their relative motion by adding the speeds of both of the objects together.

Example

​Two cyclists are moving towards each other and are about to collide on the road. If the speed of cyclist A is 5 m/s and the speed of cyclist B is $$3\ m/s$$​, what is the speed of cyclist B relative to cyclist A?

1. ​$$5 \space m/s$$​​ 2. ​$$3\space m/s$$​​​

As cyclist A and cyclist B are moving in opposite directions on the same road, you can add their speeds to calculate the relative speed of cyclist B.

​$$relative \space speed = 5 + 3$$​​

The relative speed of cyclist B is $$\underline{8\ m/s}$$​

Two objects moving in the same direction 

If two objects are moving in the same direction, then all you need to do to find the relative motion is subtract the speed of the faster object from the speed of the slower object. 

Example

​Two runners are competing in a race, the first runner is running at a speed of $$6\ m/s$$​ and the second runner at a speed of $$3\ m/s$$​. What is the speed of the first runner relative to the second?

1. ​$$6 \space m/s$$​​ 2. ​$$3 \space m/s$$​​

The relative speed is simply the speed of the first runner subtract the speed of the second runner.

$$relative \space speed = 6 - 3$$​​

The relative speed of the first runner is $$\underline{3\ m/s}$$​