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(D) $(I)$ After the collision $(t > 3 	ext{ ms})$,the final velocities of both $R$ and $S$ are positive. Since both velocities are positive,they move

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$I, II$ and $III$

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(D) $(I)$ After the collision $(t > 3 	ext{ ms})$,the final velocities of both $R$ and $S$ are positive. Since both velocities are positive,they move in the same direction.$(II)$ The total kinetic energy of the system is $K = \frac{1}{2} m_R v_R^2 + \frac{1}{2} m_S v_S^2$. For a system undergoing an elastic collision,the total kinetic energy is conserved. However,the kinetic energy of the system in the center-of-mass frame is minimum when the relative velocity is zero,which occurs at $t = 2 	ext{ ms}$ where $v_R = v_S$.$(III)$ From the graph,the change in velocity for $R$ is $\Delta v_R = 0.8 - 0.2 = 0.6 	ext{ m/s}$ and for $S$ is $\Delta v_S = 1.0 - 0 = 1.0 	ext{ m/s}$. By conservation of momentum,$m_R |\Delta v_R| = m_S |\Delta v_S|$. Since $|\Delta v_R|  m_S$. Thus,all statements are true.

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