What must the total momentum of the system be after the train cars collide?

The total momentum of the system remains the same. Momentum before collision is equal to momentum after collision

Step-by-step explanation:

Momentum is defined as the product of mass and velocity of the bodies. According to the law of conservation of momentum, a collision that occurs in an isolated system, the momentum before collision equals that after collision. After collision, the bodies can move in the same direction thus their momentum is combined.

The total momentum must remain the same.

According to the law of conservation of momentum, in a system where particles collide, the momentum loss on one particles is gained by the other one. This is what create an reaction during the collision, for example, if two bodies collide, one will decrease its speed while the other will increase its speed, that's why the momentum is conserved.

So, basically, after the train cars collide, the momentum must be conserved, remaining the same.