Two bodies A and B move in the same straight | vedclass

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(D) Let the velocity of body $A$ be $v_A = u$ (constant).Let the velocity of body $B$ be $v_B = at$ (starting from rest with acceleration $a$).Their v

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$\frac{u^2}{2a}$

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(D) Let the velocity of body $A$ be $v_A = u$ (constant).Let the velocity of body $B$ be $v_B = at$ (starting from rest with acceleration $a$).Their velocities become equal when $v_A = v_B$,which implies $u = at$. Thus,the time taken is $t = \frac{u}{a}$.The distance covered by body $A$ in time $t$ is $s_A = u \cdot t = u \left( \frac{u}{a} \right) = \frac{u^2}{a}$.The distance covered by body $B$ in time $t$ is $s_B = \frac{1}{2} a t^2 = \frac{1}{2} a \left( \frac{u}{a} \right)^2 = \frac{u^2}{2a}$.The distance between them is $d = s_A - s_B = \frac{u^2}{a} - \frac{u^2}{2a} = \frac{u^2}{2a}$.

Two bodies $A$ and $B$ move in the same straight line starting from the same position. Body $A$ moves with a constant velocity $u$ and body $B$ moves with a constant acceleration $a$ starting from rest. When their velocities become equal,the distance between them is:

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