Video Transcript
The change in the displacement of
two objects with time is shown in the graph. The gray arrows in the diagram are
the same length. Which of the following statements
about the speeds and velocities of the two objects is correct? (A) Their speeds are the same, but
their velocities are different. (B) Both their speeds and
velocities are the same. (C) Their velocities are the same,
but their speeds are different. (D) Both their speeds and
velocities are different.
This question is asking us about
the speeds and velocities of two objects whose motion is shown on a
displacement–time graph. We can see that the two objects,
red and blue, start at different positions. The blue object starts at some
positive value of displacement and the red at some negative displacement value.
Let’s recall that the velocity of
an object is given by the slope of its line on a displacement–time graph. Two lines with equal slopes
therefore correspond to two objects moving with equal velocities. We′re told that the two gray arrows
on this displacement–time graph are the same length as each other, which means that
both the red and blue lines have equal slopes to each other. In fact, we can see that both these
lines are horizontal, which means that the displacement of each object is not
changing with time. Therefore, not only do the objects
have equal velocities to each other, but both velocities are equal to zero.
Now, let’s recall that the speed of
an object is equal to the magnitude of that object’s velocity. If an object has a velocity of
zero, then it must also have a speed of zero. That means that both these two
objects must have a speed of zero, and so their speeds are also equal. We have found then that the objects
have both the same speed and the same velocity as each other, since both objects are
stationary.
The correct answer is therefore
given in option (B). Both their speeds and velocities
are the same.
