A traveller moves from A to B, where AB = D, with speed u. He turns back from B and stops at C, where AC = D/3, while returning with speed v. The ratio of average speed to magnitude of average velocity for the entire motion is:
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Question

A traveller moves from A to B, where AB = D, with speed u. He turns back from B and stops at C, where AC = D/3, while returning with speed v. The ratio of average speed to magnitude of average velocity for the entire motion is:

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G1 Physics · Accepted Answer

Forward distance AB = D. On return, BC = D − D/3 = 2D/3. Total distance = D + 2D/3 = 5D/3. Magnitude of displacement = AC = D/3. For the same total time, Average speed / |average velocity| = total distance / |displacement| = (5D/3)/(D/3) = 5. The speeds u and v cancel from this ratio.