Video Transcript
Lines A,B, andC on the
distance–time graph shown are parallel. Which of these lines could
correspond to the line shown on the speed–time graph?
Here, 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 the motion of an
object. So let’s suppose that lines A, B,
andC each represent a different moving object. What this question is asking then
is which of these objects motion could also be represented by the line that’s
plotted on the speed–time graph.
Let’s begin by taking a better look
at the distance–time graph to see what we can learn from it. Here, the vertical axis shows the
distance that the objects have traveled, and the horizontal axis shows the time that
the objects have traveled for. We know that the three lines
plotted on the graph are parallel, which means they all 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 that the line
represents. Since these lines all have the same
gradient, they must represent objects that are all moving at the same speed. We can also see that the gradient
of the lines is constant and therefore the objects all move at a constant speed.
Of course, the axes of this graph
aren’t labeled with any scales, so we can’t calculate the exact gradient of the
lines. But even though we don’t know
exactly what the gradient is, we do know that the gradient must be positive since
the lines are rising as time goes on. So because the gradient is greater
than zero, the objects must have a speed that is greater than zero. To summarize, we know that all the
lines on this distance–time graph represent objects moving at the same constant
speed that is greater than zero. Knowing this, let’s take a look at
the speed–time graph.
Similar to the other graph, the
horizontal axis represents time. But here the vertical axis
represents the speed of an object. Now notice that the red plotted
line is horizontal, meaning that its value of speed doesn’t change as time goes
on. It’s also very important to note
that the line is lying directly on the horizontal axis. Recall that this point where the
axes of a graph meet is known as the origin and it represents a value of zero on
both axes. This means that on the vertical or
speed axis, the red line corresponds to a value of zero. Therefore, this line must represent
an object that’s not moving.
As time goes on, its speed never
changes, so the object just remains at rest. So the question is whether this
line could represent the motion of any, all, or none of the objects shown by lines
A, B, andC. To answer this, let’s compare what
we learned from the two graphs. On the distance–time graph, we
found that the lines all represent objects with a constant speed that’s greater than
zero. However, the line on the speed–time
graph represents an object with a constant speed that is equal to zero. Thus, we know that the red plotted
line cannot correctly represent line A,B, orC. So our answer is that none of these
lines could correspond to the line shown on the speed–time graph.
