A 0.10-kg cart traveling in the positive x direction at 10.0 m/s collides with a 0.30-kg cart at rest. the collision is elastic. what is the velocity of the 0.10-kg cart after the collision?

By definition for an elastic shock, we have that if the second particle is at rest, then the final velocity of the first particle will be given by vf1 = ((m1-m2) * vi1) / (m1 + m2). Then, substituting the values: vf1 = ((0.1-0.3) * 10) / (0.1 + 0.4) = - 5m / s.