Under which of the following conditions is the magnitude of the average velocity of a particle moving in one dimension smaller than the average speed over some time interval? 1 pointThere are no conditions for which this is trueA particle moves in the +𝘹 direction and then reverses its directionA particle moves in the +𝘹 direction without reversingA particle moves in the −x direction without reversing
Question
Under which of the following conditions is the magnitude of the average velocity of a particle moving in one dimension smaller than the average speed over some time interval? 1 pointThere are no conditions for which this is trueA particle moves in the +𝘹 direction and then reverses its directionA particle moves in the +𝘹 direction without reversingA particle moves in the −x direction without reversing
Solution
The magnitude of the average velocity of a particle moving in one dimension is smaller than the average speed over some time interval when "A particle moves in the +𝘹 direction and then reverses its direction".
Here's why:
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Average velocity is a vector quantity that takes into account the direction of the particle's motion. It is calculated as the displacement (final position - initial position) divided by the time interval.
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Average speed, on the other hand, is a scalar quantity that only considers the total distance traveled, regardless of direction, divided by the time interval.
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If a particle moves in the +x direction and then reverses its direction, it means the particle has moved back towards its starting position. This reduces the overall displacement (because displacement considers direction), but not the total distance traveled.
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Therefore, in this case, the average speed (total distance/time) would be greater than the magnitude of the average velocity (displacement/time).
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