If two cars with identical mass collide head-on while traveling at exactly the same speed, several things will occur:
Conservation of momentum: According to Newton's third law of motion, for every action, there is an equal and opposite reaction. When the two cars collide, the force they exert on each other will be equal and opposite. As a result, their momentum will be conserved. The total momentum before the collision will be equal to the total momentum after the collision.
Deceleration and deformation: The cars will experience a sudden deceleration as a result of the collision. The kinetic energy possessed by the cars will be converted into various forms, including deformation of the cars, sound, and heat. The extent of deformation and damage will depend on various factors, such as the speed of the collision, the design and construction of the cars, and the materials involved.
Change in direction: Since the cars collide head-on, they will change their direction of motion. The angle and direction of the resulting motion will depend on the specific dynamics of the collision, including the angle of impact, the position of the center of mass of each car, and the details of the collision forces.
The specific outcome of the collision, including the damage sustained by the cars and the resulting motion, will depend on various factors such as the speed of the cars, their structural integrity, the presence of safety features, and the nature of the collision (e.g., whether it is an elastic or inelastic collision). Detailed calculations or simulations would be necessary to provide precise information about the outcome of the collision.