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Example: Two toy cars collide. - Car A: mass = 2 kg, initial speed = 4 m/s (toward Car B) - Car B: mass = 3 kg, initial speed = 0 m/s (at rest) We want to find the final speeds after the collision for both an elastic collision and a perfectly inelastic collision. Step 1: Conservation of momentum (always true). mA * vA_i + mB * vB_i = mA * vA_f + mB * vB_f Plugging values: 2 * 4 + 3 * 0 = 2 * vA_f + 3 * vB_f 8 = 2 vA_f + 3 vB_f ...(1) Step 2a: Elastic collision – also conserve kinetic energy. 0.5 * 2 * 4² + 0.5 * 3 * 0² = 0.5 * 2 * vA_f² + 0.5 * 3 * vB_f² 16 = 1 * vA_f² + 1.5 * vB_f² ...(2) Solve equations (1) and (2) simultaneously. The solution gives: vA_f = 0.8 m/s (Car A slows down) vB_f = 2.4 m/s (Car B moves forward) Step 2b: Perfectly inelastic collision – the cars stick together and move as one. Let the common final speed be v_f. 2 * 4 + 3 * 0 = (2 + 3) * v_f 8 = 5 v_f v_f = 1.6 m/s So after a perfectly inelastic collision, both cars move together at 1.6 m/s. Summary: - Elastic: Car A 0.8 m/s, Car B 2.4 m/s - Inelastic: Both cars 1.6 m/s together