Question Video: Identifying the Region of a Displacement-Time Graph in Which an Object Decreases in Speed Physics

The change of an object’s displacement with time is shown in the displacement–time graph. In which region of the graph is the speed of the object decreasing?

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Video Transcript

The change of an object’s displacement with time is shown in the displacement–time graph. In which region of the graph is the speed of the object decreasing?

On the graph, we have displacement on the vertical axis and time on the horizontal axis. On the graph, we can see an object whose displacement initially increases with time, then remains constant for a period, and finally decreases back down to zero. We’re interested in what’s happening to the object’s speed. So the key thing to recall is that speed is the magnitude of the slope of a displacement–time graph, where by magnitude we mean the positive value.

So what can we say about the speed in different segments of this graph? Well, between C and D, we can see that the line is flat, which means a slope of zero. So the speed in this region is zero. Between A and B, the line is straight. So in this region, the speed is constant. Between E and F, the line is also straight, so we also have a constant speed here. And remember that speeds can only take positive values. So what about the other two regions? Well, between B and C, we have a speed that starts at some constant positive value and ends up at zero. Therefore, between those two intervals, the speed must be decreasing. And between D and E, we have a speed that starts at zero and ends at some constant positive value and therefore must be increasing. Therefore, the region of the graph in which the speed of the object is decreasing is B to C.

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