Video: Understanding the Relation Position, Distance, and Displacement

Which of the following statements comparing position, distance, and displacement is correct? An object may record a nonzero distance while recording a displacement of zero. An object may record a distance of zero while recording a nonzero displacement. An object may record a nonzero distance while maintaining a position of zero. An object may record a nonzero displacement while maintaining a position of zero.

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Video Transcript

Which of the following statements comparing position, distance, and displacement is correct? An object may record a nonzero distance while recording a displacement of zero. An object may record a distance of zero while recording a nonzero displacement. An object may record a nonzero distance while maintaining a position of zero. An object may record a nonzero displacement while maintaining a position of zero.

In this exercise, we want to evaluate each of these four statements and find which one of the four is correct. Let’s begin with the first statement. An object may record a nonzero distance while recording a displacement of zero. That’s accurate. We can imagine an object moving in such a way that it starts and ends at the same location. And yet, it’s travelled a total distance in order to complete that journey. In that case, its distance travelled would indeed be nonzero. But its displacement, that is the separation from its start and end point, would be zero. We highlight this first statement as correct. Even though we know this is the right one, let’s continue on and look at the remaining statements. The second statement says that an object may record a distance of zero while recording a nonzero displacement. We know this statement can’t be accurate because distance is always equal to or greater than displacement.

The third statement says that an object may record nonzero distance while maintaining a position of zero. If an object maintains a position of zero, that means that it doesn’t move at all. In which case, it couldn’t record a nonzero distance. So we know this third statement is not accurate either. And finally, the fourth statement says an object may record a nonzero displacement while maintaining a position of zero. Once again, if an object maintains a position of zero, then its displacement as well as its distance cannot be anything other than zero. This means it’s unable to record a nonzero displacement. So this fourth statement is not correct either.

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