# Question Video: Using Graphs to Represent the Speed of an Object Science

Which of these graphs can show how the speed of an object changes with time? [A] Only the speed–time graph [B] Only the distance–time graph [C] Both graphs [D] Neither graph

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### Video Transcript

Which of these graphs can show how the speed of an object changes with time? (A) Only the speed–time graph, (B) only the distance–time graph, (C) both graphs, (D) neither graph.

In this question, we’re shown a speed–time graph and a distance–time graph. The speed–time graph shows directly how the speed of an object, plotted on the vertical axis, changes with time, plotted on the horizontal axis. So we know that a speed–time graph does show how the speed of an object changes with time.

Now, what about a distance–time graph? This shows how the distance of an object, plotted on the vertical axis, changes with time, plotted on the horizontal axis. Let’s recall that the speed of an object is equal to the distance traveled divided by the time taken to travel the distance. On a distance–time graph, the slope is equal to the change in distance traveled, the vertical coordinate, divided by the change in time taken, the horizontal coordinate. Notice that this is equal to our expression for the speed of an object. That means that the slope of a distance–time graph gives us the speed of the object.

So, by observing how the slope of the graph changes with the horizontal coordinate, time, we can use a distance–time graph to see how the speed changes with time. Therefore, a distance–time graph also shows how the speed of an object changes with time. Our answer then is option (C). Both graphs can show how the speed of an object changes with time.