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? (A) Line 𝐵 only, (B) line 𝐵 and
line 𝐶 only, (C) line 𝐴, line 𝐵, and line 𝐶, (D) line 𝐶 only, or (E) none of
these lines.
In this question, we are asked to
relate the information given to us on a distance–time graph to a speed–time
graph. First, let’s think about the
distance–time graph. We have the three lines, 𝐴, 𝐵,
and 𝐶, drawn on a distance–time graph where the horizontal axis represents time and
the vertical axis represents distance. The lines are all horizontal. Let us think about what this
means. If a line on a distance–time graph
is horizontal, it means that all the values of time on the 𝑥-axis correspond to the
same distance on the 𝑦-axis.
For example, let’s compare the
distance represented by line 𝐴 at two different times, 𝑡 one and 𝑡 two. These two times correspond to
different positions on the 𝑥-axis, but they correspond to the same position on the
𝑦-axis. This means that, at both times, the
object represented by line 𝐴 is the same distance from whatever reference point
we’re measuring from. We could do this for any of the
times on the 𝑥-axis. The object represented by this line
is always at the same distance from the reference point. So, a horizontal line on a
distance–time graph represents an object which is always at the same distance from
the reference point.
On our distance–time graph, lines
𝐴, 𝐵, and 𝐶 are all horizontal. The only difference between them is
that they have different vertical positions. Line 𝐴 corresponds to the largest
value on the 𝑦-axis and so represents an object at a greater distance from a
reference point than line 𝐵 or 𝐶. In fact, line 𝐶 corresponds to
zero distance, meaning line 𝐶 represents an object that is still at the reference
point.
We’ve now seen that a horizontal
line on a distance–time graph represents an object that is always at the same
distance from the reference point. Let’s think about what this tells
about the speed of the objects represented by lines 𝐴, 𝐵, and 𝐶. If the distance of each object from
the reference point never changes, this tells us that none of the objects are
moving. They must all be stationary. And if an object is stationary, it
means that its speed is zero. So, the three lines on this
distance–time graph all represent objects that have zero speed.
Now let’s consider what the
speed–time graph for each of these objects would look like. On a speed–time graph, time is
represented by the horizontal axis and speed is represented by the vertical
axis. In the same way that a horizontal
line on a distance–time graph represents a constant distance, a horizontal line on a
speed–time graph represents a constant speed. We know that lines 𝐴, 𝐵, and 𝐶
from the distance–time graph all represent objects with zero speed. An object with a speed of zero is
represented by a horizontal line that runs along the horizontal axis at speed
zero. This is exactly what we see drawn
in the graph given to us in the question.
So, we know that all three lines
𝐴, 𝐵, and 𝐶 drawn on the distance–time graph represent objects that have a
constant speed of zero. The line on the speed–time graph
also represents an object which has a speed of zero. So, any of the lines on the
distance–time graph could correspond to the line drawn on the speed–time graph. The answer is therefore option (C):
line 𝐴, line 𝐵, and line 𝐶.
