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Under what condition (s) is the magnitud...

Under what condition (s) is the magnitude of average velocity of an object is equal to its average speed ?

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If an object moves in a straight line in the same direction, then the magnitude of average velocity of an object is equal to its average speed.
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The magnitude of average velocity is equal to the average speed when a particle moves:-

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Assertion: The magnitude of average velocity of the object over an interval of time is either smaller than or equal to the average speed of the object over the same interval. Reason: Path length (distance) is either equal or greater than the magnitude of displacement.

Define : Average speed

A man walks on a straight road from his home to a market 2.5 km away with a speed of 5 km h^(-1). Finding the market closed, he instantly turns and walks back home with a speed of 7.5 km h^(-1). What is the (a) magnitude of average velocity, and (b) average speed of the man over the interval of time (i) 0 to 30 min, (ii) 0 to 50 min, (iii) 0 to 40 min ? [Note: You will appreciate from this exercise why it is better to define average speed as total path length divided by time, and not as magnitude of average velocity. You would not like to tell the tired man on his return home that his average speed was zero !]

Explain clearly, with examples, the distinction between : (a) magnitude of displacement (sometimes called distance) over an interval of time, and the total length of path covered by a particle over the same interval, (b) 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 onedimensional motion only).

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