Video Transcript
The changes of displacement of two
objects with time are shown in the graph. The lines plotted on the graph are
parallel. Which one 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) Their velocities are the same,
but their speeds are different. (C) Both their speeds and
velocities are different. (D) Both their speeds and
velocities are the same.
This question has given us a
displacement–time graph. And we are asked to compare the
speeds and velocities of the two objects whose motion is shown on this graph.
Let’s recall that the velocity of
an object is equal to the slope of its line on a displacement–time graph. We are told that the lines that
represent the motion of the red and blue objects are parallel. Though the two objects start at
different displacement values, the fact that the two lines are parallel means that
they have the same slope. And so the two objects have the
same velocity as each other.
Now, the velocity of an object is a
vector quantity; that is, it has both a magnitude and a direction. Two objects with equal velocities
must each have velocities with the same magnitude and the same direction as each
other. Unlike velocity, speed is a scalar
quantity. That means it has only a magnitude
and no direction. The speed of an object is equal to
the magnitude of its velocity. Since we’ve established that the
magnitude of the velocity of both these two objects is the same, then we know that
the two objects must both have the same speed. We have found then that the two
objects in this question have both the same speed as each other and the same
velocity as each other.
The correct answer is, therefore,
given by option (D). Both their speeds and velocities
are the same.
