### Video Transcript

The graph is a displacement–time graph for an object. At which of the labeled points on the graph does the object have the greatest speed?

If we take a look at our graph, we can see displacement on the vertical axis and time on the horizontal axis. The red line shows an object that starts with a displacement of zero. This displacement increases for the first seven and a half or so seconds until it reaches a maximum and then decreases back down to zero by the end. Now we need to recall how to find the speed from a displacement–time graph. Speed is the magnitude of the slope of a displacement–time graph. So what we need to find in this question is at which of the labeled points is the magnitude of the slope of this graph the greatest?

Now, the keyword to pick out here is magnitude. The magnitude means the positive value, so it doesn’t matter if the slope is positive or negative. We’re looking for the point where the positive value of that slope would be the greatest. So let’s look back at our graph. The red line starts off flat, which means that the object is stationary or has a speed of zero. It then gradually speeds up reaching a peak value up this side and then turns over, which means it’s slowing down. Then the slope goes to zero, which means it’s instantaneously at rest. It then speeds up again reaching its peak value again down this side, then gradually slowing down, and eventually coming to a stop.

So there are two segments of this graph where the object is at its highest speed. There’s one segment on this side as the displacement is increasing and then another segment on the other side as the displacement is decreasing. Within these two segments, there is only one labeled point. So the answer to the question “at which of the labeled points on the graph does the object have the greatest speed?” is point D.