Cars Colliding Then Skidding | Linear Momentum | Friction | Kinematics

Two cars travelling in opposite directions collide inelastically, sticking to each other. After colliding the cars slide down the road, skidding to a stop as a result of friction acting between the tires of the cars and the road.
The solution to the problem is rooted in the conservation of linear momentum as well as Newton's 2nd Law and the kinematic equations.
This problem commonly comes up in introductory physics courses such as High School Physics, AP Physics, early college mechanics and serves as the foundation for problems found on the JEE and A Level Exams.