Assertion (A): The displacement of a vertical | vedclass

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(C) Let the initial velocity of the body be $u$. The time taken to reach the maximum height is $t = \frac{u}{g}$. At maximum height,the final velocity

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$(A)$ is true but $(R)$ is false

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(C) Let the initial velocity of the body be $u$. The time taken to reach the maximum height is $t = \frac{u}{g}$. At maximum height,the final velocity $v = 0$.The displacement in the last second of upward motion is the same as the distance covered in the first second of downward motion starting from rest at the maximum height.Using the equation of motion $s = ut + \frac{1}{2}at^2$,for the first second of downward motion ($u = 0$,$a = g$,$t = 1$ s):$s = 0(1) + \frac{1}{2}g(1)^2 = \frac{g}{2}$.Thus,Assertion $(A)$ is true.Reason $(R)$ is false because for a body moving under gravity,the acceleration is constant $(g)$ and directed downwards throughout the motion; it does not decrease.

Assertion $(A)$: The displacement of a vertically projected body during the last second of its upward motion is $\frac{g}{2}$.
Reason $(R)$: For a vertically projected body,the acceleration decreases gradually and becomes $\frac{g}{2}$ during the last second of upward motion.

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Assertion $(A)$: The displacement of a vertically projected body during the last second of its upward motion is $\frac{g}{2}$.Reason $(R)$: For a vertically projected body,the acceleration decreases gradually and becomes $\frac{g}{2}$ during the last second of upward motion.