Both vehicles experience the same change in momentum.
When the compact car rear ends a truck, they exert equal forces on each other, in accordance with Newton's third law. The force exerted by the car on the truck is equal to the force exerted by the truck on the car.The force acting on the two bodies act for the same interval of time.
According to Newton's second law, the force acting on a body is equal to the rate of change of momentum.
Since the forces are equal,
therefore, the change in momentum of the car is equal to the change in the momentum of the truck
.
Thus, both the car and the truck experience the same change in their momentum. However due to the smaller mass of the car, the change in its velocity is greater than the change in the truck's velocity, which has a larger mass.