Video Transcript
The distance–time graph shows an
object moving at a constant speed. What is the speed of the
object?
In this question, we’ve been asked
to find the speed of the object represented by the line on this distance–time
graph. Let’s begin by looking at the graph
and see what we can figure out from it. Notice that the vertical axis shows
the distance in meters that the object has traveled, while the horizontal axis shows
the time in seconds that the object travels for. Looking closer at the axes, we can
see that the side length of each grid square represents 10 meters along the vertical
axis and 10 seconds along the horizontal axis.
Now, let’s take a look at the line
on this graph and figure out what speed it represents. We should recall that the speed
represented by a straight line on a distance–time graph, like we have here, is equal
to the gradient of the line. Thus, if we simply work out the
gradient of the line, we’ll have determined the speed of the object. We should recall that we measure
the gradient of a line between two points.
Here, we know that the object has a
constant speed, and thus the line on the graph has a constant gradient. This means that we can choose to
measure the gradient between any two points along the line of motion. Let’s choose these two points
marked in pink. Now, the gradient of a line on a
distance–time graph is equal to the change in distance divided by the change in time
between the two points that we’ve chosen. This, of course, is also equal to
the speed of the object. In order to calculate, let’s first
work out the change in distance.
We know that this point corresponds
to a distance of zero meters and this point corresponds to a distance of 10
meters. So, the change in distance between
these two points is equal to 10 meters minus zero meters, which is just equal to 10
meters. Next, let’s work out the change in
time. We know that this point corresponds
to a time of zero seconds and this point corresponds to a time of 10 seconds. So, the change in time between
these two points is equal to 10 seconds minus zero seconds, or just 10 seconds.
Now, let’s substitute these values
into our formula for speed. And we have 10 meters divided by 10
seconds, which simplifies to one meter per second. So, we have our answer. The speed of the object represented
by the line on the distance–time graph is one meter per second.
