Explain clearly, with examples, the distinction between: Magnitud… - Vidyadip

Question

Explain clearly, with examples, the distinction between: Magnitude of average velocity over an interval of time, and the average speed over the same interval. [Average speed of a particle over an interval of time is defined as the total path length divided by the time interval]. Show in both (a) and (b) that the second quantity is either greater than or equal to the first. When is the equality sign true? [For simplicity, consider one-dimensional motion only]

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Answer

Magnitude of average velocity = Magnitude of displacement/Time interval For the given particle, Average velocity = AC/t Average speed = Total path length/Time interval = (AB + BC)/t Since (AB + BC) > AC, average speed is greater than the magnitude of average velocity. The two quantities will be equal if the particle continues to move along a straight line

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