Video Transcript
An object does not move during a
time interval. What must the displacement of the
object in that time interval be? (A) The displacement could have any
value. (B) The displacement must be
zero.
In this question, we are asked to
consider the displacement of an object that doesn’t move during a time interval. Recall that displacement is the
shortest straight-line distance from an object’s starting point to its endpoint. So, if an object starts out at this
position and ends up at this position, then this arrow represents its
displacement. In this case, however, the object’s
starting point is the same as its endpoint because the object doesn’t move at
all. Since the end and start positions
are, in fact, the same position, then there is no distance between the start point
and endpoint. The displacement therefore has a
magnitude of zero.
Recall that displacement is a
vector quantity. That means it has a magnitude and
also a direction. For a vector with a magnitude of
zero, the direction is not a well-defined property. We would simply say, in this case,
that the displacement is zero. We have found then that since the
object didn’t move during the time interval and thus the endpoint is in exactly the
same place as the start point that the displacement of the object is zero. Therefore, the correct answer is
option (B). The displacement must be zero.
