Question Video: Comparing the Motion of Two Objects Plotted on the Same Distance-Time Graph

The red and blue lines show the change in distance moved for two objects. Which color line corresponds to the object that moves the greater distance? [A] The blue line [B] The red Line [C] Both objects move the same distance

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Video Transcript

The red and blue lines show the change in distance moved for two objects. Which color line corresponds to the object that moves the greater distance? Is it (a) the blue line, (b) the red Line, or (c) both objects move the same distance?

If we look at our graph, we can see that distance is on the vertical axis. So what we’re looking for is which object has increased its value on the vertical axis the most. We first check their starting positions and note that both objects start at the same distance. So whichever has the higher value at the end will have covered the greater distance overall. If we trace the ending values of the blue and red lines back to the vertical axis, we can see that the blue line ends at a higher value. Therefore, the object that moves the greater distance is that represented by (a) the blue line.

The next part of the question asks, “Which color line corresponds to the object that moves at the greater average speed?” Is it (a) the blue line, (b) the red line, or (c) both objects move at the same average speed?

To answer this question, we need to recall that average speed is equal to the total distance divided by the total time. So to have a greater average speed, you either need your total distance to be greater or the total time taken to cover that distance to be smaller. We know from the first part of the question that the greater distance is covered by the blue line. For the total time taken, we need to look at the horizontal axis of the graph. If we trace the endpoints of the two lines down to the horizontal axis, we can see that the blue line ends at a smaller time value than the red line. So the blue line has a smaller total time value.

So the object corresponding to the blue line covers a greater distance and does so in a smaller amount of time than the object corresponding to the red line. Therefore, the answer to the question, “Which color line corresponds to the object that moves at the greater average speed?” is (a) the blue line.

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