### Video Transcript

Which of these graphs can show how
the speed of an object changes with time? (A) Only the speed–time graph, (B)
only the distance–time graph, (C) both graphs, (D) neither graph.

In this question, we’re shown a
speed–time graph and a distance–time graph. The speed–time graph shows directly
how the speed of an object, plotted on the vertical axis, changes with time, plotted
on the horizontal axis. So we know that a speed–time graph
does show how the speed of an object changes with time.

Now, what about a distance–time
graph? This shows how the distance of an
object, plotted on the vertical axis, changes with time, plotted on the horizontal
axis. Let’s recall that the speed of an
object is equal to the distance traveled divided by the time taken to travel the
distance. On a distance–time graph, the slope
is equal to the change in distance traveled, the vertical coordinate, divided by the
change in time taken, the horizontal coordinate. Notice that this is equal to our
expression for the speed of an object. That means that the slope of a
distance–time graph gives us the speed of the object.

So, by observing how the slope of
the graph changes with the horizontal coordinate, time, we can use a distance–time
graph to see how the speed changes with time. Therefore, a distance–time graph
also shows how the speed of an object changes with time. Our answer then is option (C). Both graphs can show how the speed
of an object changes with time.