Velocity of a body on reaching the point from which it was projected upwards, is:

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Accepted Answer

1. **Initial Conditions:** A body is projected vertically upwards with an initial velocity $u$. Let the upward direction be positive ($+$) and the downward direction be negative ($-$). Thus, initial velocity is $+u$.
2. **Displacement Condition:** When the body reaches the point of projection, the net displacement ($s$) is zero because the final position coincides with the initial position.
3. **Apply Kinematic Equation:** Use the third equation of motion $v^2 = u^2 + 2as$ .
   - Substituting $s = 0$, we get:
     $$ v^2 = u^2 + 2a(0) $$
     $$ v^2 = u^2 $$
     $$ v = \pm u $$
4. **Determine Sign:** Since the body is moving downwards while returning to the projection point, its velocity must be negative (opposite to the direction of projection). Therefore, the final velocity is $v = -u$. The magnitude (speed) remains the same, but the direction is reversed .

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