Video Transcript
Select the velocity–time graph that
best matches the following description of motion. A boat moves at constant speed
through the water, then accelerates for a short time, and then continues moving at a
higher constant speed.
In this question, we are presented
with five different velocity–time graphs. And we want to find the
velocity–time graph that best matches the description of motion given in the
question. Let’s break up the description of
motion into smaller parts, and we will consider how each part of the description
will be represented on a velocity–time graph.
The boat initially moves at a
constant speed through the water. If an object is moving at a
constant speed, then this means that the object’s velocity must have a constant
magnitude. On a velocity–time graph, a
velocity with a constant magnitude will be represented by a straight horizontal line
parallel to the time axis. For a line like this, all the
different time values on the 𝑥-axis correspond to the same value of velocity on the
𝑦-axis.
If we look at the five
velocity–time graphs, we can see that graphs (A), (B), and (D) do not initially
begin with a straight horizontal line. Instead, these three graphs begin
with lines that have a constant positive gradient. This shows the velocity the boat
increasing with time, which means that the boat would be accelerating during this
time interval. This does not match the initial
description of motion for the boat, so this means that graphs (A), (B), and (D) are
incorrect. Graphs (C) and (E) do begin with a
straight horizontal line parallel to the time axis, so these two graphs match the
initial description of motion.
The next part of the description
says the boat accelerates for a short time. On a velocity–time graph, this
would be represented by a line with a positive gradient. As the time value increases on the
axis, so does the value of the velocity. In graph (C), this part of the
graph is straight and has a positive gradient, which indicates a constant value of
acceleration. In graph (E), the line is curved
but still maintains a positive gradient throughout. This corresponds with a changing
value of acceleration. The description of motion does not
say whether the acceleration of the boat is constant or changing, so graphs (C) and
(E) still match the description of motion up to this point.
Now let’s consider the final part
of the description of motion, which says the boat continues to move at a higher
constant speed. Similar to the initial part of the
description of motion, a constant speed will mean that the boat’s velocity must have
a constant magnitude, which corresponds to a straight horizontal line parallel to
the time axis on a velocity–time graph. However, the boat is now moving at
a higher constant speed than it was at the start. This means that the straight
horizontal line should be higher up on the velocity axis than the line representing
the boat’s initial motion.
In graph (E), this final line has a
constant positive gradient indicating that the boat is accelerating during this time
interval. This does not match the final part
of the description of motion for the boat, so graph (E) is incorrect. Graph (C) does have a straight
horizontal line during this final motion. This horizontal line is higher than
the horizontal line representing the boat’s initial motion, which indicates a higher
constant speed. This matches the final part of the
description of motion, and so graph (C) must be the correct answer. Graph (C) best matches the
description of motion.
