A perfectly inelastic collision occurs when two objects collide and stick together after the impact, moving as a single entity. In this type of collision, the total momentum of the system is conserved, but kinetic energy is not. This means that while the momentum before and after the collision remains the same, some energy is transformed into other forms, such as heat or sound. An example of a perfectly inelastic collision is when two cars, represented by Car A and Car B, crash into each other and become entangled. After the collision, they move together at a common velocity, which is determined by their combined masses and the initial velocities of both cars.