Video Transcript
The distance–time graph shows an
object moving at a uniform speed. What is the speed of the
object?
For this question, we’ve been asked
to find the speed of the object represented by the line on this distance–time
graph. We can see that the vertical axis
represents distance, and each mark along this axis represents one meter
traveled. The horizontal axis represents
time, and each mark along this axis represents one second.
Now, let’s take a look at the line
on this graph and figure out what speed it represents. To do this, recall that on a
distance–time graph, the speed of an object corresponds to the gradient of the line
representing its motion. This means we can work out the
speed of the object by determining the gradient of the line. In this question, we’re told that
the object has a uniform speed, meaning the value of its speed doesn’t change. Thus, the object is represented by
a line with a constant gradient.
Recall that we measure the gradient
of a line between two points on the line. Here, we can choose to measure the
gradient between any two points along this line because the gradient is the same
throughout the entire line. Let’s calculate the gradient
between 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 we’ve chosen. Of course, this is also equal to
the speed of the object.
To calculate the speed, 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 one
meter. So the change in distance between
these two points is equal to one meter minus zero meters, which is just equal to one
meter. 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 one second. So the change in time between these
two points is equal to one second minus zero seconds, which is just equal to one
second.
Now, let’s substitute these values
into the formula for speed. We have that the speed of our
object is equal to one meter divided by one second, or simply one meter per
second. This is the final answer. The speed of the object shown on
the distance–time graph is one meter per second.
