Work-Energy Theorem
The work done by the net force acting on a particle equals the change in its kinetic energy:
$$W_{\text{net}} = \Delta K = K_f - K_i = \frac{1}{2}m v_f^2 - \frac{1}{2}m v_i^2$$
Elastic 1D Collision:
Coefficient of restitution $e = 1$:
$$v_1 = \left(\frac{m_1 - m_2}{m_1 + m_2}\right)u_1 + \left(\frac{2m_2}{m_1 + m_2}\right)u_2$$
