Assertion (A): A body is thrown vertically upwards with an initial speed \( 25 \text{ m/s} \) from a position 1. It falls back to position 1 after some time. During this time duration, total change of velocity of the body is zero.
Reason (R): Average acceleration of the body during this time is zero.
Solution:
Assertion (A) is false. Initial velocity is \( +25 \text{ m/s} \). Final velocity at the same position is \( -25 \text{ m/s} \). The change in velocity is \( \Delta \vec{v} = (-25) - (+25) = -50 \text{ m/s} \). Reason (R) is false. Since the change in velocity \( \Delta vec{v} \) is not zero, and \( \Delta t \) is a finite time, the average acceleration \(\ vec{a}_{avg} = \frac{\Delta \vec{v}}{\Delta t} \) is also not zero. It is \( -g \).
Therefore, both the Assertion and the Reason are false.
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