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 about a
displacement–time graph, and we are asked about the speeds and velocities of the two
objects whose motion is shown on this graph. We can see that the two objects,
red and blue, start at the same position, a displacement of zero. The blue object then moves in the
direction of positive displacement, while the red object moves in the negative
direction.
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 can see that the blue line has a
positive slope, while the red line has a negative slope. This means that the direction of
each object’s velocity is different. Since velocity is a vector quantity
with both a magnitude and a direction, then two velocities are only equal if they
have both the same magnitude and the same direction. Since in this case the directions
are different, we know that the two objects do not have the same velocity as each
other.
We are told that these two gray
arrows have the same length. That means that, in a given amount
of time, the blue object travels the same distance in the positive direction as the
red object travels in the negative direction. This means that the magnitudes of
the velocities of the two objects are equal. Let’s now recall that an object’s
speed is equal to the magnitude of its velocity. Since these two objects have equal
magnitudes of their velocities, then we know that they have equal speeds.
So we have found then that the
objects have the same speed as each other, but they have different velocities. The correct answer is therefore
given in option (A). Their speeds are the same, but
their velocities are different.
