Calculating the Final Speed of Inelastically Colliding Carts: Physics Problem Solution

In an inelastic collision where the two objects stick together after the collision, we can use the principle of conservation of momentum. The initial momentum of the system is equal to the final momentum. The momentum (p) is calculated as the mass (m) times the velocity (v). The initial momentum is the sum of the momenta of the two carts before the collision. For the 3 kg cart: p1_initial = m1 * v1 = 3.00 kg * 4.00 m/s = 12.00 kg*m/s. For the 5 kg cart: p2_initial = m2 * v2 = 5.00 kg * 2.00 m/s = 10.00 kg*m/s. Total initial momentum = p1_initial + p2_initial = 12.00 kg*m/s + 10.00 kg*m/s = 22.00 kg*m/s. After the collision, the two carts stick together and move as one object, so their total mass is m1 + m2 = 3.00 kg + 5.00 kg = 8.00 kg. The final momentum of the system is also 22.00 kg*m/s (because momentum is conserved). We can set the final momentum (mass times velocity) equal to the initial total momentum and solve for the final velocity. So, 8.00 kg * v_final = 22.00 kg*m/s. Therefore, v_final = 22.00 kg*m/s / 8.00 kg = 2.75 m/s. So, the speed of the two carts (moving together) after the collision is 2.75 m/s.