An assembled system consists of cart A of inertia \(m_{A}\), cart B of inertia \(m_{\mathrm{B}}\), and a spring of negligible inertia, clamped together so that the fully compressed spring is aligned between the front end of cart B and the back end of cart A. The internal energy of the system, stored in the compressed spring, is \(E_{\text {spring }}\). The system is put on a lowfriction track and given a small shove so that it moves to the right at speed \(v_{\mathrm{i}}\), with cart \(\mathrm{A}\) in front. Once the system is moving, the clamp is released (by remote control, so that the motion of the system as a whole is not affected in any way). As the spring expands, the carts move apart. What are their final speeds?