Video Transcript
Which of the following corresponds
to a horizontal line on a speed–time graph? Is it (A) an object that travels in
a horizontal direction, (B) an object at rest, or (C) an object that travels at any
constant speed?
Let us consider a pair of axes for
a speed–time graph where the horizontal axis represents time and the vertical axis
represents speed. We can add a horizontal line to
this graph, for example, a line that represents a speed, equal to three meters per
second. We can see that for increasing
values of time shown along the horizontal axis, the value of speed shown on the
vertical axis is a constant three meters per second, neither increasing nor
decreasing. The only thing that this line shows
is that the object that has had its motion represented by the graph travels a
distance of three meters in each one-second time interval shown on the graph.
The direction in which the object
travels three meters in any particular time interval is not something that the graph
can show. A distance can be traveled in any
direction, even changing directions. The fact the line on the graph is
horizontal does not mean that the object has horizontal motion. This is because a line on a
speed–time graph does not show the shape of the path that the object travels
along.
We can see that option (A) cannot
be correct. Option (A) says that the graph
shows that an object travels in a horizontal direction. But the graph does not show
anything about the direction of motion of the object.
Option (B) says that a horizontal
line on a speed–time graph shows an object that is at rest, meaning an object that
does not move. An object that does not move does
not change the distance that it travels. Option (B) might then seem correct
because a horizontal line on the graph shows a value on the 𝑦-axis of the graph
that does not change.
Let us consider again the example
of the horizontal line with a constant value for speed of three meters per
second. The object that has motion
represented by this line moves three meters in each one-second time interval shown
on the graph. An object that is at rest would
have to travel zero distance in a time interval, not a distance of three meters. We could replace the horizontal
line with a constant value for speed of three meters per second with a horizontal
line with a constant value for speed of zero meters per second. This would represent an object that
is not moving. We can see then that there is one
particular horizontal line that represents an object at rest, but all other
horizontal lines do not represent an object at rest.
Option (C) says that a horizontal
line on a speed–time graph shows an object that travels at a constant speed. We have seen that a horizontal line
on a speed–time graph can show a constant speed of three meters per second. And we have also seen that a
horizontal line on a speed–time graph can show a constant speed of zero meters per
second. A horizontal line on a speed–time
graph can in fact show any constant speed. Whatever the vertical axis value of
the line is on a speed–time graph is the constant speed shown by the line, so option
(C) is correct.
