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(A) In a one-dimensional elastic collision between two bodies of equal mass $(m_1 = m_2 = m)$,the bodies exchange their velocities.Let the initial vel

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$V$

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(A) In a one-dimensional elastic collision between two bodies of equal mass $(m_1 = m_2 = m)$,the bodies exchange their velocities.Let the initial velocities be $u_1 = V$ and $u_2 = 0$.According to the conservation of linear momentum:$m u_1 + m u_2 = m v_1 + m v_2$$V + 0 = v_1 + v_2$$v_1 + v_2 = V$  --- $(1)$According to the conservation of kinetic energy for an elastic collision:$\frac{1}{2} m u_1^2 + \frac{1}{2} m u_2^2 = \frac{1}{2} m v_1^2 + \frac{1}{2} m v_2^2$$V^2 = v_1^2 + v_2^2$  --- $(2)$From $(1)$,$v_2 = V - v_1$. Substituting this into $(2)$:$V^2 = v_1^2 + (V - v_1)^2$$V^2 = v_1^2 + V^2 + v_1^2 - 2 V v_1$$2 v_1^2 - 2 V v_1 = 0$$2 v_1 (v_1 - V) = 0$This gives $v_1 = 0$ (the case where no collision occurs) or $v_1 = V$.Since the first body was at rest and the second body hit it,the first body acquires the velocity of the second body,which is $V$.

$A$ body of mass $m$ is at rest. Another body of the same mass moving with velocity $V$ makes a head-on elastic collision with the first body. After the collision,the first body starts to move with velocity:

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