Video Transcript
What quantities do the axes of a
distance–time graph correspond to? Is it (A) the distance moved by an
object and the speed of the object? (B) The speed of an object and the
time for which the object moves. Or (C) the distance moved by an
object and the time for which the object moves.
Let’s begin by drawing an example
of a distance–time graph. In this graph, we see two plotted
lines, which represent the motion of two different objects. Now this question is asking us
about the information that’s given by the graph’s axes. Our three answer options give
different combinations of three different quantities: distance, speed, and time.
To think about this, we can recall
how to use a distance–time graph to learn about an object’s speed. Let’s take a closer look at the
graph. We notice that both the orange and
pink lines begin at the same time value. They also both end at the same time
value. Therefore, both lines represent the
same change in time. However, we can see that the pink
line has a greater slope than the orange line. We know that both lines begin at
the same distance value, but the pink line rises up higher along the vertical axis
than the orange line does. Therefore, the pink line shows a
greater change in distance than the orange line.
To think about what this tells us
about the object’s speed, we can recall that speed is equal to distance divided by
time. Our distance–time graph shows that
over the same amount of time, the object whose motion is shown in pink travels a
greater distance than the object shown in orange. Therefore, the pink line shows a
greater speed than the orange line. So we’ve seen how the slope of a
line on a distance–time graph represents speed. But in order to even use the speed
formula, we have to interpret information from both axes on the distance–time
graph.
And this question is basically
asking us “What do the axes represent?” Recall that we use the vertical
axis to learn about the distance that the objects moved and the horizontal axis to
learn about the time it took for the objects to move. The actual speeds of the objects
were not given by either axis of our distance–time graph. So the correct answer is option
(C). The axes of a distance–time graph
correspond to the distance moved by an object and the time for which the object
moves.
