The red and blue lines show the change in distance moved with time for two objects. The dotted black arrows shown are the same length. Which color line corresponds to the object that increases its distance more? Is it (a) the blue line, (b) the red line, or (c) both objects increase their distance by the same amount?
On the graph shown, distance is given on the vertical axis. So what we’re trying to find is which of the two lines has moved furthest on the vertical axis. We can see that the blue line moves the greatest distance in total. However, it also started at the greatest distance. The separation between the two objects at the start is given by this black arrow. And this black arrow, at the end, we’re told is the same length.
The bottom of the second black arrow is in line with the final distance of the red line. So if the two objects had covered the same total distance, the blue line would end up the same distance above the red line that it was to start with. But instead, we see that the blue line has covered less distance than this. Therefore, the object that has increased its distance more is represented by the red line.