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Provide clear explanations and examples to distinguish between: ( a ) The total length of a path covered by a particle and the magnitude of displacement over the same interval of time. ( b ) The 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]. In ( a ) and ( b ) compare and find which among the two quantity is greater. When can the given quantities be equal? [For simplicity, consider one-dimensional motion only].
Provide clear explanations and examples to distinguish between: ( a ) The total length of a path covered by a particle and the magnitude of displacement over the same interval of time. ( b ) The 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]. In ( a ) and ( b ) compare and find which among the two quantity is greater. When can the given quantities be equal? [For simplicity, consider one-dimensional motion only].
CBSE | Class 11 | Motion in a Straight Line | Motion in a straight line | NCERT | Physics | Physics
Provide clear explanations and examples to distinguish between: ( a ) The total length of a path covered by a particle and the magnitude of displacement over the same interval of time. ( b ) The 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]. In ( a ) and ( b ) compare and find which among the two quantity is greater. When can the given quantities be equal? [For simplicity, consider one-dimensional motion only].

Answer –

(a) Consider a football, which is passed to player B by player A and then immediately kicked back to player A along the same path. The magnitude of the ball’s displacement is now 0 because it has returned to its original position. The overall length of the path travelled by the ball, however, is AB + BA = 2AB. As a result, the first quantity is clearly greater than the second.

( b ) Assume, in the foregoing example, that a football player covers the complete distance in t seconds. Then, the magnitude of the ball’s average velocity throughout time intervals. t = Displacement magnitude/time interval

t = 0 / = 0

The ball’s average speed during the same time interval is equal to the whole length of the path divided by the time interval.

= 2AB/t

As a result, the second quantity exceeds the first.

If the ball simply moves in one direction from one player to another, the above values are equivalent (considering one-dimensional motion).

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