Video Transcript
Lines A, B, and C on the
distance–time graph shown are parallel. Which of these lines could
correspond to the line shown on the speed–time graph?
In this question, we’ve been given
a distance–time graph with three lines plotted on it and a speed–time graph with one
plotted line. Before we begin, recall that we can
use distance–time graphs and speed–time graphs to represent an object’s motion. So, for the remainder of this
question, let’s suppose that lines A, B, and C each represent a different moving
object.
This question is asking then, which
of these objects’ motion could also be represented by the red line on the speed–time
graph? To think about this, let’s first
take a better look at the distance–time graph. Here, the vertical axis shows us
the distance the objects have traveled, and the horizontal axis shows the time the
objects have traveled for. We know that the three plotted
lines are parallel, which means they all must have the same gradient or slope.
Recall that on a distance–time
graph, the gradient of a line is equal to the speed of the object whose motion the
line represents. So, since these lines all have the
same gradient as each other, they must all represent objects that are moving at the
same speed as each other. Also notice that none of the
objects is changing speed at any time. All three lines have a constant
gradient, and therefore all three objects must be moving at a constant speed. It’s good to note too that the
lines are staggered or spaced apart because there is some amount of distance
separating each object from the other. So the three objects are moving at
the same speed, just with a little bit of distance between them.
Knowing this, let’s jump over to
the speed–time graph and see if we can figure out which of the lines A, B, and C
could also be represented by this red line here. Similar to the other graph, this
horizontal axis tells the time that an object is traveling for. But notice that here the vertical
axis represents the speed that an object is traveling. Now, we can see that the line on
this graph is horizontal. So let’s recall that on a
speed–time graph, a horizontal line corresponds to an object whose value of speed
doesn’t change as time goes on. That means that this line must
represent an object moving at a constant speed.
So the question is whether this
line could represent the motion of any, all, or none of the three objects shown by
lines A, B, and C. Well, we know that the red line
must represent an object moving at a constant speed, which is also true of each of
the three lines on the distance–time graph. So it could very well represent the
objects shown by line A, line B, and line C. Since all three have the same
constant speed, line A, line B, and line C could all correspond to the line shown on
the speed–time graph.
