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? (A) Yes or (B) no.
This question asks us whether or
not these two arrows, red and blue, have the same displacement. Recall that a displacement is the
vector along an object’s shortest path from start to finish. It has a magnitude and a
direction. So, really, this question is asking
us two things. That is, do the arrows point in the
same direction? And do they have the same length
from start to finish, which would be the shortest path the car can take from the
center to the circumference?
For an object in the center of a
circle, it needs to travel the length of the radius of the circle to reach the
circle’s circumference. We see in this case that both the
red and blue arrows extend from the center of the circle to a point on the circle’s
circumference. We can say then that each arrow is
a radius of the circle. And if the car were to travel along
either path, it would reach the circle’s circumference. There is no shorter path the car
could travel to reach the circumference. Therefore, both arrows represent
the shortest path from start to finish and can be defined as the magnitude of the
displacement.
Also, since the arrows overlap
entirely, we can say that they point in the same direction. Let’s look at our displacement
checklist. Does each arrow cover the shortest
distance from start point to endpoint? The answer is yes. Does each arrow point in the
direction of motion? Once again, the answer is yes.
We can therefore conclude that both
arrows have the same displacement. Option (A) is correct.
