Video Transcript
When an object has a speed that
does not change throughout its motion, what will the line representing the motion
look like on a distance–time graph? (A) Curved, (B) either straight or
curved, (C) straight.
To answer this question, let’s
begin by recalling that the speed of an object can be calculated using the formula
speed equals the distance traveled by the object divided by the time it takes the
object to travel that distance.
Now, we’re being asked about what a
nonchanging speed looks like when the motion is represented on a distance–time
graph. Let’s recall that a distance–time
graph plots distance traveled on the vertical axis against time on the horizontal
axis. Because speed is equal to distance
divided by time and a distance–time graph gives us information about both distance
and time, then we can use a distance–time graph to work out things about an object’s
speed.
We are being asked about an object
that has a speed that doesn’t change. We call this a constant speed. Our job is to work out what a
distance–time graph looks like for an object moving with a constant speed. To help us think about this, let’s
add a scale to our distance–time graph axes and draw the distance–time graph for an
object moving with a constant speed of one meter per second. If an object moves with a constant
speed of one meter per second, this means that it moves a distance of one meter in
every one second of time. At the instant we start measuring
the motion of the object, zero seconds have passed and the object has traveled zero
meters.
We can show this information on our
graph by adding a point here at zero, zero. After one second has passed, the
object will have moved one meter. We can show this on the graph by
adding another point here at one, one. After a further second, so at a
time of two seconds, the object will have traveled another meter, taking its total
distance traveled to two meters. Let’s add this point at two, two to
our graph. In the same way, after three
seconds, the object will have traveled a distance of three meters. And after four seconds, it will
have traveled four meters.
We have now drawn a few points on
our distance–time graph for an object moving at a constant speed of one meter per
second. To make the graph easier to
understand, we can join these points together using a single line. Then looking at this line, we can
notice something very important. The line is straight. We’ve found then that for this
particular example of an object moving at a constant speed of one meter per second,
the motion is represented by a straight line on a distance–time graph. Now, we have only shown this for
one particular speed. But it turns out that the same is
true for any constant speed.
Recall that the speed of an object
is equal to the distance it has traveled, which is the quantity plotted on the
vertical axis of the graph, divided by the time it takes to travel the distance,
which is the quantity plotted on the horizontal axis. We know that for straight-line
graphs, the slope of a line is equal to the change in the vertical coordinate
divided by the change in the horizontal coordinate. For a distance–time graph, these
coordinates are distance and time, respectively. So, for a distance–time graph, the
slope is equal to the distance divided by the time. And so the slope of a straight line
on a distance–time graph is equal to the speed of the object. This means that any constant speed
must be represented on a distance–time graph by a line with a constant slope.
For a line to have a constant
slope, it must be a completely straight line. Different constant speeds can be
represented by straight lines with different slopes. A faster moving object will
correspond to a steeper line, while a slower moving object will correspond to a
shallower line. But no matter the actual value of
the speed, a constant speed will always correspond to a straight line on a
distance–time graph.
The correct answer is therefore
option (C). If an object does not change speed
throughout its motion, then the line representing the motion on a distance–time
graph will be straight.
