Calculating the Final Speed of Two Colliding Carts Post-Inelastic Collision

The principle of conservation of momentum states that for two objects colliding, the total momentum before the collision equals the total momentum after the collision. Before the collision, the total momentum is the sum of the momentum of the two carts, which is (mass1 * velocity1) + (mass2 * velocity2). So, the total momentum before the collision is: (3.00 kg * 4.00 m/s) + (5.00 kg * 2.00 m/s) = 12.00 kg*m/s + 10.00 kg*m/s = 22.00 kg*m/s. Since the two carts stick together after the collision, their combined mass after the collision is 3.00 kg + 5.00 kg = 8.00 kg. Therefore, according to the conservation of momentum, the velocity of the combined carts after the collision is the total momentum before the collision divided by the combined mass. So the velocity (speed, as we don't consider direction in speed) after the collision is: 22.00 kg*m/s / 8.00 kg = 2.75 m/s.