Inelastic Collision of Carts: Calculating Final Speed Post-Collision

The problem involves the concept of conservation of momentum for inelastic collisions. According to this concept, the total momentum before the collision equals the total momentum after the collision. The total momentum before the collision equals the sum of the momenta of the two carts. The momentum (p) of an object is given by the product of its mass (m) and velocity (v): p = mv. The total initial momentum (p_initial) is: p_initial = (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 carts stick together after the collision, their combined mass becomes (3.00 kg + 5.00 kg) = 8.00 kg. Let's denote the final speed of the carts after the collision as vf. According to the conservation of momentum, the total initial momentum must equal the total final momentum. Therefore: p_initial = p_final, then 22.00 kg*m/s = 8.00 kg * vf. Now let's solve this equation for vf: vf = 22.00 kg*m/s / 8.00 kg = 2.75 m/s. So, the speed of the carts after they collide is 2.75 m/s.