Video Transcript
The distance–time graph shows an
object moving at a constant speed. What is the speed of the
object?
Here, we’ve been given a
distance–time graph of an object in motion and we want to find the speed of this
object. So let’s begin by taking a closer
look at the graph. We can see that the vertical axis
shows the distance the object travels in meters and the horizontal axis shows the
time that the object has been traveling for in seconds. Now, to answer this question, let’s
recall that the speed represented by a straight line on a distance–time graph is
equal to the gradient of the line. The gradient of a line is always
measured between two points. And since this object has a
constant speed, the line on the graph has a constant gradient. So we can choose to measure the
gradient between any two points along this line.
Here, we’ll choose these two points
marked in pink. Now, the gradient of a line on a
distance–time graph, and therefore the speed of the object whose motion the line
represents, is equal to the change in distance divided by the change in time between
the two points that we’ve chosen. First, let’s find the change in
distance between the points. We can see that this point here
corresponds to a distance of zero meters and this point here corresponds to a
distance of six meters. Therefore, the change in distance
between these two points is equal to six meters minus zero meters, which is just
equal to six meters.
Now, let’s find the change in time
between the two points. We can see that this point here
corresponds to a time of zero seconds and this point corresponds to a time of three
seconds. So the change in time between these
two points equals three seconds minus zero seconds, or just three seconds.
Now that we’ve determined the
change in distance traveled and the change in time between the two points on the
line, we can calculate the speed of the object. So, substituting these values into
the formula for speed, we have six meters divided by three seconds. Six divided by three simplifies to
two, and we’re working in units of meters per second. So we have our final answer. The speed of the object represented
by the line on the distance–time graph is two meters per second.
