Examples of invariant are momentum, angular momentum, and energy. Momentum is an invariant , i.e. it does not change unless an external force acts on it. Momentum being a vector, each direction is conserved independently. This is called conservation of momentum . In the case of a rocket flight both m and v change.
Impulse is the product of force time during which the force is applied.
Suppose two cars collide head on and stick together. The only external force is that of friction between the cars and the road. During the split second the cars collide, D t is effectively 0, so momentum is conserved. The total momentum is conserved. The mass after collision is 2,500kg.