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Question Video: Identifying Changes in Speed on a Distance–Time Graph Science

Which of the following distance–time graphs shows an object initially moving with constant speed that stops moving and then starts moving again with a lesser constant speed. [A] Graph A [B] Graph B

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Video Transcript

Which of the following distance–time graphs shows an object initially moving with constant speed that stops moving and then starts moving again with a lesser constant speed. Is it graph (A) or graph (B)?

Let’s look closely at the two graphs at the same time and see what they describe.

We can see that each graph shows a line. For each graph, the line starts at the origin. And for each graph, the line changes direction twice. We can define some points: point zero, point one, point two, and point three. We can refer to these points when describing the ways that the lines on the graphs change. Point zero is the origin of the graph. Point one is where the line first changes direction. Point two is where the line next changes direction. And point three is the end of the line.

Both graphs show a straight line from point zero to point one. And this tells us that both graphs represent an object moving at a constant speed in a time interval. In both graphs, the line from point one to point two is horizontal; that is, the distance does not change. So we know that the objects represented by both graphs have stopped moving.

So far, the answer could be either graph, so it comes down to the final part of the movement. The question asks, which object has a speed when it starts to move again that is less than the initial speed of the object? We know speed is represented by the slope of a distance–time graph. So we’re looking for which graph has a lesser slope between point two and point three than between point zero and point one. We can see that the slope for graph (B) is less for between point two and point three than it is between point zero and point one. And so we know the correct answer is option (B).

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