Video Transcript
Which of the following
distance–time graphs shows an object that initially accelerates and then
decelerates?
We’ve been given three options to
choose from: (A), (B), and (C). In order to figure out which one of
these distance–time graphs shows an object that accelerates and then decelerates, we
just need to remember one rule. The slope of the line on a
distance–time graph is equal to the speed of the object. With this in mind, let’s look at
the variation of the slope of the line on each of these graphs. In each case, we’ll start by
looking on the left of the graph, which corresponds to the start of the object’s
journey. And we’ll see how the slope of the
line changes as we move forwards in time.
Let’s start with option (A). We can see that this graph is made
up of two straight-line segments. The first of these is both straight
and sloped. In other words, it has a constant
slope. Since this rule tells us that the
slope of the line is equal to the speed of the object, this line segment with a
constant slope indicates that the object has a constant speed. So for the first part of the
journey shown in option (A), the object moves with a constant speed.
For the next part of the object’s
journey, the graph is just a straight horizontal line. Since the graph is horizontal, this
means that slope is zero. And because the slope of the line
is equal to the speed of the object, that means that this section of the graph shows
the object is stationary. So overall, graph (A) shows us an
object which initially travels at a constant speed and then immediately comes to a
stop. It doesn’t show us an object that
accelerates and then decelerates. So we know that option (A) is not
the correct answer.
Let’s take a look at graph (B). We can see that the first part of
this graph is curved upward. This means that the slope of the
line is increasing as we move forward in time. And we know from this rule that if
the slope of the line is increasing, then the speed of the object must be
increasing. In other words, the first part of
this graph shows us an object which is accelerating. Now, although this graph initially
curves upward, we can see that this changes and later on it curves the other
way. We can say that at this part of the
graph, the slope is decreasing. And if the slope is decreasing,
then the object’s speed must be decreasing. We can say that at this point, the
object is decelerating. So it looks like option (B) is the
correct answer. But let’s take a quick look at
option (C) just to be sure.
Now, the first part of this graph
is actually a straight line, which means that the object represented by this graph
is initially traveling at a constant speed. Next, the graph curves in such a
way that its slope decreases. So this portion of the graph shows
us that the object’s speed is decreasing, in other words, is decelerating. The last section of this graph is
also a straight line, showing us that the object again travels at a constant speed,
although we know that it’s traveling slower than it was previously because the slope
here is less steep than the slope here.
But overall we can see that graph
(C) does not match the description of motion given in the question. So we can now be sure that option
(B) is the right answer. The fact that the slope of this
graph initially increases and then decreases means that it shows us an object which
initially accelerates and then decelerates.
