### Conservation of Momentum in One Dimension

When there is an absence of an external force on a system, momentum is conserved. This means that a system's initial and final momentums are the same. However, objects within a system may have different initial and final momentums. This is usually exemplified through a collision.

In any one-dimensional collision, two objects are colliding. When you see train cars colliding into each other, for example, you would often see that the initial car slows down and that the second car takes up speed. This just means that the first car loses its momentum because some of it is transferred over to the second car. As a system, friction is negligible. Therefore, the total momentum doesn’t change. The momentum of the first car before the collision is the same as the combined momentum of the two cars after the collision.

### Creative Applications

1. What is the inherent assumption in this scenario?

2. Why is it that the train car scenario is an example of conservation of momentum in one direction?

3. Develop an equation to model this scenario. (Hint: the momentum of any object is mv)