Video Transcript
A car is at the center of a
circle. The arrows show the 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 wants us to consider
whether two paths that have the same starting and ending points could have the same
displacement. To answer this question, we must
recall the definition of displacement.
The displacement of an object is
the shortest distance from the start point to the endpoint of the motion of the
object. The displacement also denotes the
direction of motion. We see that the blue path is a
straight path. So it is the shortest distance the
car could travel from start to finish. Therefore, the magnitude or length
of the blue arrow is the magnitude of the car’s displacement.
Furthermore, since the blue path is
a straight line that stretches from the center of a circle to a point on the
circle’s circumference, we can say its length is equal to the radius of the
circle. On the other hand, the magnitude of
the displacement of a car traveling along the red path is not equal to the distance
traveled along the red path. This is because the red path is
curved. Recall that displacement is always
straight line motion. In fact, the magnitude of the red
path’s displacement is the same as for an object on the blue path.
However, that’s not all we have to
consider. An object’s displacement also
describes an object’s direction of motion. We can see clearly that though the
two arrows end up at the same spot, they do not always point in the same
direction. For the first part of its journey,
a car traveling along the red path would be traveling to the right of its starting
point, before veering sharply to the left and ending up at the same point on the
circumference of the circle as a car traveling along the blue path.
The direction of both paths’
displacement, however, is the same. The direction of both displacements
is in the direction of the blue arrow. Since the magnitudes of both
displacements are the same as well, we have found that while the distances are not
the same, both displacements in this question are exactly the same. Therefore, answer choice (A) is
correct.
