A car is moving on a straight road at 84 kilometres per hour, and in the opposite direction, a motorbike is moving at 45 kilometres per hour. Suppose the direction of the car is positive. Find the velocity of the motorbike relative to the car.
In order to answer this question, it is worth drawing a diagram first. We know that the direction of travel of the car is positive, and it is travelling at 84 kilometres per hour. The motorbike is moving in the opposite direction with a velocity of 45 kilometres per hour. As the bike is moving in the opposite direction, we can say that the car has a velocity of positive 84 and the bike has a velocity of negative 45.
Let’s consider these two numbers on a number line, as shown. We need to work out the velocity of the motorbike relative to the car. This means we need to work out how we would get to negative 45 from 84. As we’re moving to the left or down on the number line, the relative velocity will be negative. To get from 84 to zero, we subtract 84. And to get from zero to negative 45, we subtract another 45.
Negative 84 minus 45 is equal to negative 129. We can therefore say that the velocity of the motorbike relative to the car is negative 129 kilometres per hour. If both vehicles started from the same point, after one hour, they would be 129 kilometres apart. This means that the motorbike would be 129 kilometres in the negative direction relative to the car.