3. a 2,000-kilogram railroad car moving at 5 m/sec to the east collides with a 6,000-kilogram railroad car moving at 3 m/sec to the west. if the cars couple together, what is their velocity after the collision?

So we wan't to know what is the velocity after a collision of two railroad cars, one moving to the east and the other moving to the west if m1=2000kg, v1=5m/s and m2=6000kg, v2=3m/s. We can find the solution using the law of conservation of momentum for plastic collisions that states that the momentum must remain constant before (left side of the equation) and after (right side of the equation) the collision: m1*v1+m2*v2=(m1+m2)*v. So now we simply plug in the numbers and get: 2000kg * 5m/s + 6000kg * 3m/s = (2000kg + 6000kg)*v. Now we can write: 10000 kgm/s + 18000 kgm/s = 8000kg * v. To get v, the velocity of both railroad cars after the collision we simply divide both sides of the equation with 8000 kg: so v=3.5m/s to the west.