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Question Video: Comparing Distances Shown on a Distance–Time Graph Science

Which of the lines on the distance-time graph represents the object that travels the greater distance?

04:09

Video Transcript

Which of the lines on the following distance–time graph represents the object that travels the greater distance? Is it (A) line 𝐴, (B) line 𝐵, or (C) both objects traveled the same distance?

We begin by recalling that for a distance–time graph as shown here, the horizontal axis represents the time for which an object travels and the vertical axis represents the distance that the object travels. A line on a distance–time graph, for which in this case there are two, shows how the distance traveled by an object changes with the time that the object travels for. This question asked us to compare the motion of two objects that are represented by two different lines. These lines are called line 𝐴 and line 𝐵.

We can see that line 𝐵 is longer than line 𝐴. And we might think that this means line 𝐵 represents an object that travels a greater distance. However, this is not the correct way to answer this question. A line on a graph does not show the shape of the path that an object travels along, and a longer line does not necessarily mean a greater distance traveled. Let us instead consider what a line on a distance–time graph does mean. As already mentioned, time is represented by the horizontal axis. And taking this into consideration, we should consider that a line has two ends. One end of a line has a smaller value of time than the other end. And the end with the lesser value of time shows where and when the motion of the object represented by the line starts.

The end of the line with the greater value of time shows where and when the motion of the object represented by the line ends. Since time is represented by the horizontal axis, this means that the greater the change in the value of the horizontal axis between the ends of a line, the greater the time that the object represented by the line moved for. And as distance is represented by the vertical axis, the greater the change in the value of the vertical axis between the ends of a line, the greater the distance that the object represented by that line moved.

In this question, we are asked which line represents the object that travels the greater distance. The question does not ask anything about the time for which either object travels. As such, we only need to look at the changes in the value on the vertical axis at the ends of the lines. We can see that the value of distance is the same for the ends of both line 𝐴 and of line 𝐵 that show the start of the motion. Both lines have ends that touch but do not cross the origin of the graph. These must represent the same distance for the start of motion.

We can also see that the value of distance is the same for the ends of both line 𝐴 and line 𝐵 that show the end of motion. This time, both lines have ends that touch but do not cross the dashed horizontal line. This dashed horizontal line represents a value of distance. And as the ends of both lines touch but do not cross the horizontal line, the value of distance for the end of motion for both lines is also the same. We can therefore conclude that the correct answer is option (C). The objects represented by line 𝐴 and by line 𝐵 moved the same distance.

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