Question Video: Comparing the Speeds and Velocities of Objects Using a Displacement-Time Graph

The changes of displacement of two objects with time are shown in the graph. The lines plotted on the graph are parallel. Do the two objects have the same velocity? Do the two objects have the same speed?

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Video Transcript

The changes of displacement of two objects with time are shown in the graph. The lines plotted on the graph are parallel. Do the two objects have the same velocity? And do the two objects have the same speed?

If we look at our graph, we see that it shows displacement versus time. There are two lines plotted on our graph: one represented by the red line, so we’ll call the red object, starts with an initial displacement of zero and increases at a constant rate over time to some positive value. The other object, which we’ll call the blue object as it’s represented by a blue line, starts with some positive displacement and also increases at a constant rate to some higher positive displacement.

Now we need to recall the definition of velocity, which is that velocity is displacement over time. On this graph, that means the velocity is given by the vertical value divided by the horizontal value or, in other words, that velocity is the slope of a line on this graph. Now, although there are no values marked on these axes, we are told in the question that the two lines are parallel, which is another way of saying that they have the same slope. If two objects have the same slope on a displacement–time graph, that means they have the same velocity. Therefore, the answer to the question “Do the two objects have the same velocity?” is yes.

Now, for the second part of the question “Do the two objects have the same speed?” It’s helpful to remember here from the definition of velocity as a vector, velocity has both magnitude and direction. And then another term for the magnitude of velocity is speed. So we already found in the first part of the question that the two objects have the same velocity. This means they have to have both the same magnitude and the same direction. And if they have the same magnitude, they must have the same speed. Therefore, the answer to the question “Do the two objects have the same speed?” is yes.

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