A 0.5 kg cart moving at 4 m/s crashes into a 1.5 kg cart at rest. The two carts end up stuck together. What is the speed of the two carts after the collision?

The final speed of the two carts is 1 m/s.

Explanation:

let m = 0.5 kg being the mass of the cart moving at an intial speed of v = 4 m/s and M = 1.5 kg is the mass of the cart at rest V = 0 m/s.

then by conservation of linear momentum, the final speed of the objects Vf is:

m*v + M*V = Vf * (M + m)

Vf = [m*v + M*V] / (M + m)

Vf = [ (0.5 kg) * (4 m/s) + (1.5 kg) * (0 m/s) ] / (1.5 + 0.5 kg)

= 1 m/s

Therefore, the final speed of the two carts is 1 m/s.