Final answer:
In both elastic and inelastic collisions, the total momentum before the collision is equal to the total momentum after the collision due to the law of conservation of momentum. However, only in an elastic collision is kinetic energy also conserved.
Step-by-step explanation:
The law of conservation of momentum states that the total momentum of a closed system remains constant over time, which applies to both elastic and inelastic collisions. In an elastic collision, both momentum and kinetic energy are conserved, meaning the total momentum before the collision is equal to the total momentum after the collision, and kinetic energy is also conserved. In contrast, an inelastic collision conserves momentum but not kinetic energy; some kinetic energy is converted to other forms of energy, such as heat or sound, but the total momentum before and after the collision remains the same.
For example, if two cars collide elastically and one is moving while the other is at rest, the total momentum after the collision will be the same as the momentum of the moving car before the collision. If they collide inelastically and stick together, they will move as one object after the collision with the same total momentum that was present before the collision, indicating that momentum is conserved in both scenarios.