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Question Video: Comparing the Distances Moved by Two Objects Science

Consider the graph. The motion of object A is represented by the solid line. The motion of object B is represented by the dashed line. Which of the following statements correctly compares the distances moved by the objects? [A] Object B travels the greater distance [B] Object A travels the greater distance [C] The distances moved are equal?

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Video Transcript

Consider the following graph. The motion of object A is represented by the solid line. The motion of object B is represented by the dashed line. Which of the following statements correctly compares the distances moved by the objects? Is it (A) object B travels the greater distance, (B) object A travels the greater distance, or (C) the distances moved are equal?

Recall that for a distance–time graph, 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 shows how the distance traveled by an object changes with time that the object travels for. This question asks us to compare the motion of two objects that are represented by two different lines, a solid blue line and a red dashed line.

Recall that time is represented by the horizontal axis. Taking this fact into consideration, we should consider that a line has two ends. One end of the line has a smaller value of time than the other end of the line. The end of the line with a lesser value of time shows where and when the motion of the object represented by the line starts. The end of the line with a greater value of time shows where and when the motion of the object represented by the line ends.

Recall again that time is represented by the horizontal axis, and consider that distance is what is represented by the vertical axis. This means that the greater the change in the value of the horizontal axis between the ends of the line, the greater the time that the object represented by the line moved for. This also means that the greater the change in the value of the vertical axis between the ends of the line, the greater the distance that the object represented by the line moved. Let us make sure to avoid the mistake of thinking that the length of a line on a distance–time graph shows the shape of the path traveled by an object.

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. Because we are only considering the distances that objects travel, to find the distances that the objects represented by the lines travel, we only need to look at the changes in the value on the vertical axis of the ends of the lines. If we look closely, we can find which line has the greater value on the vertical axis. This is clearly object B. So we know object B has traveled a greater distance than object A. So the correct answer is option (A). Object B travels the greater distance.

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