Question

The Law of Conservation of Momentum states that Momentum between two moving

objects is conserved when those two objects collide.
Consider the following:
Two cars are moving in the same direction, one behind the other. The rear car is moving
with a momentum of 50 kg*m/s, and the front car moves with a momentum of 100
kg*m/s. The cars have a combined momentum of 150 kg*m/s.
The rear car HITS the car in front of it, but no brakes or other stopping forces are
applied. The rear car's momentum changes to 40 kg*m/s. What is the new momentum
front car?

Answer 1

As stated, the momentum of the system is conserved during the collision (even the kinetic energy is not - some energy is lost to heat, deformation, etc)

M1 V1 = M2 V2 expresses momentum conservation

150 kg-m/s = (40 + X) kg-m/s

X = 110 kg-m/s is the new momentum of the front car

More specifically,

M1 V1 + M2 V2 = M1 V1' + M2 V2'