Video Transcript
A car is at the center of a
circle. The arrows show paths that the car
could travel to reach the circumference of the circle. Is the displacement of the car
between its initial and final positions the same in both cases? Is it (A) yes or (B) no?
This question asks us to consider
whether the displacement along both the red and blue paths is the same. This is a straightforward question
so long as we recall the definition of displacement. The displacement of an object is
the shortest path from an object’s starting point to its ending point. The displacement includes a
description of the direction the object traveled.
Let’s consider the car traveling
along the blue path. This path is a straight line from
the center of the circle to the circumference of the circle. This means the blue path is also
the length of the circle’s radius. Since the blue path is straight, it
must be the shortest distance from the start point to the endpoint. This means that the magnitude of
the displacement in this case is also the length of the blue path. We also note that the blue path’s
displacement points in the direction of the blue arrow.
Next, we can consider the red
path. It, too, is a straight line that
points from the circle’s center to its circumference. We can say then that the length of
the red path is also the length of the circle’s radius. Since the red path is a straight
line, it must be the shortest path the car can travel. Therefore, we can also say that the
magnitude of the car’s displacement along the red path is the length of the red
path. Finally, we note that the red
path’s displacement points in the direction of the red arrow.
So we’ve noticed two things: one
that the magnitude of the car’s displacement along both the red and blue path is the
same. That is, it is the length of the
circle’s radius. And two, the displacements point in
different directions. The red path and the blue path do
not point in the same direction. Because the directions are
different, we must say that the displacements of the two paths are different. The correct answer is option (B),
no.
