Question Video: Identifying the Instantaneous Speed of an Object at a Point on a Curve on a Displacement-Time Graph Physics • First Year of Secondary School

Video Transcript

The graph shows the displacement of a motorcycle in a race along a straight track. At which of the labeled points on the graph does the motorcycle have the greatest speed?

The graph shows time in seconds along the horizontal axis and displacement in meters along the vertical axis. Now recall how we find speed. Speed is the magnitude of the slope of a displacement–time graph. So to find the point with the greatest speed, we need to know at which point is the magnitude of the slope of this graph the greatest.

And we can do this by eye. We can see that the graph starts off with a relatively shallow slope around point 𝐴 and the slope gets steeper as we move along in time, which means the motorcycle is speeding up and traveling faster at later times so that by the time we get to point 𝐸 the slope of the graph is the greatest. So the answer is that the motorcycle has the greatest speed at point 𝐸.