Video Transcript
Which of the lines on the following
distance–time graph represents the object that travels the greater time? Is it option (A) line 𝐴, option
(B) line 𝐵, or option (C) both objects traveled the same amount of time?
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 asks us to compare
the motion of two objects that are represented by the two different lines. These are called line 𝐴 and line
𝐵.
We can see from the graph that line
𝐴 is longer than line 𝐵. And we might think that this means
that line 𝐴 represents an object that travels for a greater time. This is not the correct way to
answer this question, however. In order to answer this question,
we recall once again 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. And 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.
In the same way, 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. Recalling once again that time is
represented by the horizontal axis and distance 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.
In this question, we are asked
which line represents the object that travels for the greater time. The question does not ask anything
about the distance that either object travels. As such, we only need to look at
the changes in the value on the horizontal axis. We can see that the value of time
is the same for the ends of both line 𝐴 and of line 𝐵 that show the start and end
of the motion. Both lines have ends that touch but
do not cross the origin of the graph. These must represent the same time
for the start of the motion. Likewise, both lines have ends that
touch but do not cross the dashed vertical line. This line represents a value of
time. And as the ends of line 𝐴 and line
𝐵 both touch but do not cross the vertical line, the value of time for the end of
motion for both lines is the same.
We can therefore conclude that the
correct answer is option (C). The objects represented by line 𝐴
and by line 𝐵 traveled for the same amount of time.
