Momentum in Action: Calculating the Post-Collision Speed of Two Carts

In an inelastic collision where the objects stick together, the principle of conservation of momentum can be used to solve the problem. The principle of conservation of momentum states that the total momentum before the collision equals the total momentum after the collision. The equation for momentum is p = mv, where p = momentum, m = mass, and v = velocity. Initial total momentum = Final total momentum Initial momentum of the first cart (before collision) = m1v1 = 3kg * 4m/s = 12 kg*m/s. Initial momentum of the second cart (before collision) = m2v2 = 5kg * 2m/s = 10 kg*m/s. Initial total momentum = 12 kgm/s + 10 kgm/s = 22 kgm/s. After the collision: Let's assume the final velocity (speed) for both carts (since they stick together and move as a single object) to be v_f. Final total momentum = (m1 + m2) * v_f Using conservation of momentum, we can equate this to the initial total momentum: Initial total momentum = Final total momentum So we have, 22 kg*m/s = (3kg + 5kg) * v_f 22 = 8 * v_f Solving for v_f, we get, v_f = 22 / 8 = 2.75 m/s. So, the speed of the carts after the collision is 2.75 m/s.