Two carts of equal mass are on a horizontal, frictionless air track. Initially cart A is moving toward stationary cart B with a speed of va. The carts undergo an inelastic collision, and after the collision the total kinetic energy of the two carts is one-half their initial total kinetic energy before the collision. What is the speed of each cart after the collision?

v_{f} = v / 2

Explanation:

In this problem we will define a system formed by the two cars, in this case the forces during the collision are internal and the momentum is conserved.

Initial instant. Before the collision

        p₀ = m v

final instant. After the inelastic collision

        = (m + m) v_{f}

the moment is preserved

        p₀ = p_{f}

        m v = 2m v_{f}

        v_{f} = v / 2

since the cars have an inelastic collision the speed of the two vehicles is the same

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