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Question Video: Comparing the Displacements of Two Similar Paths Science

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?

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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.

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