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 time traveled by the objects? Is it (A) object B travels the
greater time? (B) Object A travels the greater
time. Or is it (C) object A and object B
travel an equal amount of time?
Recall that for a distance–time
graph, the horizontal axis represents the time for which an object travels. The vertical axis represents the
distance that the object travels. Then, a line on a distance–time
graph shows how the distance traveled by an object changes with the 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.
Since time is represented by the
horizontal axis, if we take this into account, we should consider that a line has
two ends. One end of a line has a smaller
value of time than the other end of the line. The end of the line 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.
Now let’s consider that distance is
what is represented by the vertical axis. We now see 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. This also means that 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’re essentially
asked which line represents the object that travels for the greater time. The question doesn’t ask us
anything about the distance for which either object travels. Because we’re only considering the
times that the objects travel for, to find the times that the objects represented by
the lines travel for, we only need to look at the changes in the value on the
horizontal axis of the ends of the lines.
If we look closely, we can find
which line has the greater value on the horizontal axis. This is clearly object A. So we know that object A has
traveled for a greater time than object B.
So the correct answer is option
(B). Object A travels the greater
time.
