Distance-Time vs Displacement-Time Graphs

Plotting both graphs for the same motion shows the difference between distance and displacement. Distance is a scalar and can only increase, while displacement is a vector and can increase, decrease or become negative.Consider a ball thrown vertically upwards and caught at the same height. On the way up, the distance travelled and the displacement are the same, so the two graphs are identical until the ball reaches its maximum height.At the maximum height the gradient of the displacement-time graph is zero, because the velocity is zero. After this the ball falls back, so its displacement decreases until it is zero when the ball is caught.The distance keeps increasing on the way down, so the distance-time graph continues to rise. After the top, it is a reflection of the displacement-time graph. By the end the total distance is twice the maximum height, while the displacement is zero.