Two carts on a frictionless track: Cart A (m1 = 2 kg) moves right at 3 m/s, Cart B (m2 = 3 kg) moves left at 1 m/s. They collide elastically.\n\nStep 1: Find centre‑of‑mass velocity (v_cm).\n v_cm = (m1*v1 + m2*v2) / (m1+m2) = (2*3 + 3*(-1)) / 5 = (6 - 3)/5 = 0.6 m/s to the right.\n\nStep 2: Transform to CM frame (subtract v_cm).\n v1_cm = v1 - v_cm = 3 - 0.6 = 2.4 m/s (right).\n v2_cm = v2 - v_cm = -1 - 0.6 = -1.6 m/s (left).\n\nStep 3: Use elastic‑collision formula in CM frame: speeds simply reverse.\n v1_cm' = -v1_cm = -2.4 m/s (now left).\n v2_cm' = -v2_cm = 1.6 m/s (now right).\n\nStep 4: Transform back to lab frame (add v_cm).\n v1' = v1_cm' + v_cm = -2.4 + 0.6 = -1.8 m/s (left).\n v2' = v2_cm' + v_cm = 1.6 + 0.6 = 2.2 m/s (right).\n\nResult: After the elastic collision, Cart A moves left at 1.8 m/s, Cart B moves right at 2.2 m/s.