The figure shown is a velocity–time graph for two cars moving in a straight line. The movement of car 𝐴 is represented by the green line and the movement of car 𝐵 by the blue line. Determine how long it took for the two cars to meet again, given that they started from the same point.
As the two cars started at the same point and we need to work out when they meet again, this will occur when the displacement of car 𝐴 is equal to the displacement of car 𝐵. When dealing with a velocity–time graph, the displacement can be calculated by working out the area between the line and the 𝑥-axis. In order to do this, we would usually require values on the 𝑥-axis for time and values on the 𝑦- or vertical axis for velocity.
In this question, however, we have no values on the 𝑦-axis. We do notice, however, that the point at which the two lines cross after 14 seconds is halfway between the start point and the endpoint of the graph at 28 seconds. We recall that the area of any triangle is half the area of a corresponding rectangle with the same dimensions. This means that the area shaded in orange must be equal to the area shaded in pink. We can, therefore, conclude that the area of the green rectangle is equal to the area of the blue triangle. This means that after 28 seconds, car 𝐴 and car 𝐵 will have the same displacement from the origin. We can, therefore, conclude that the two cars will meet again after 28 seconds.