A 1000 kg car moving at 20 m/s collides with a 2000 kg truck that is initially at rest. After the collision, they stick together and move with a common velocity. What is the velocity of the combined vehicles after the collision?

Core Concept

This is a perfectly inelastic collision where momentum is conserved but kinetic energy is not. Initial momentum = m_car * v_car + m_truck * v_truck = 1000 kg * 20 m/s + 2000 kg * 0 m/s = 20,000 kg·m/s. After collision, combined mass = 1000 kg + 2000 kg = 3000 kg. Using conservation of momentum: initial momentum = final momentum, so 20,000 kg·m/s = 3000 kg * v_final. Therefore, v_final = 20,000 kg·m/s / 3000 kg = 6.67 m/s.