Final answer:
The velocity of the combined mass of the two carts after the collision is 2 m/s, derived using the principle of conservation of momentum in an inelastic collision.
Step-by-step explanation:
The question relates to a conservation of momentum problem in a physics context, where two carts collide and stick together in a perfectly inelastic collision. Since external forces (negligible friction) do not affect the system, the momentum before the collision will be equal to the momentum after the collision. According to the conservation of momentum, the formula pbefore = pafter can be applied, where p represents momentum, which is the product of mass and velocity (p = m*v).
For the provided scenario, the initial momentum of the system is calculated using the momentum of the moving cart (2 kg moving at 3 m/s) plus the momentum of the cart at rest (1 kg at 0 m/s). Therefore, pbefore = 2 kg * 3 m/s + 1 kg * 0 m/s = 6 kg*m/s. After the collision, the total mass of the combined carts is 2 kg + 1 kg = 3 kg. As the two carts stick together and move with a common velocity, we need to find this velocity vafter.
Applying momentum conservation: pbefore = pafter, we get 6 kg*m/s = 3 kg * vafter, which upon solving gives vafter = 2 m/s. Therefore, the correct answer is (b) 2 m/s.