To solve this problem we will apply the concepts related to the conservation of momentum. That is, the final momentum must be the same final momentum. And in each state, the momentum will be the sum of the product between the mass and the velocity of each object, then
Here,
= Mass of each object
= Initial velocity of each object
= Final velocity of each object
When they position the final velocities of the bodies it is the same and the car is stationary then,
Rearranging to find the final velocity
The expression for the impulse received by the first car is
Replacing,
The negative sign show the opposite direction.