A railroad freight car, mass 15,000 kg, is allowed to coast along a level track at a speed of 2.0 m/s. It collides and couples with a 50,000-kg second car, initially at rest and with brakes released. What is the speed of the two cars after coupling?

Newton's second law in terms of momentum:  The rate of change of momentum of an object is equal to the net force applied to it.
The law of conservation of momentum: The total momentum of an isolated system of objects remains constant.

Newton's second law for a system of particles: The sum of all forces acting on the system is equal to the total mass of the system times the acceleration of its center of mass.