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(C) In a head-on elastic collision between two particles of identical mass where one is initially at rest,the particles exchange their velocities.Let

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$P$ comes to rest and $Q$ moves forward with speed $v$

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(C) In a head-on elastic collision between two particles of identical mass where one is initially at rest,the particles exchange their velocities.Let the mass of both particles be $m$.Initial velocity of $P$ is $u_1 = v$ and initial velocity of $Q$ is $u_2 = 0$.Using the conservation of linear momentum: $mv + m(0) = mv_1 + mv_2 \implies v = v_1 + v_2$.Using the property of elastic collision (coefficient of restitution $e = 1$): $v_2 - v_1 = e(u_1 - u_2) = 1(v - 0) = v$.Solving the two equations:$v_1 + v_2 = v$$v_2 - v_1 = v$Adding these gives $2v_2 = 2v \implies v_2 = v$.Substituting back gives $v_1 = 0$.Therefore,$P$ comes to rest and $Q$ moves forward with speed $v$.

$A$ particle $P$ moving with speed $v$ undergoes a head-on elastic collision with another particle $Q$ of identical mass but at rest. After the collision:

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