Final answer:
An elastic collision is one where total kinetic energy and momentum are conserved. It is often easier to analyze an elastic collision, and the relationship between relative velocities before and after collision is typically verified mathematically.
Step-by-step explanation:
Understanding Elastic Collisions
An elastic collision is a type of collision where the total kinetic energy and total momentum of the system are conserved. In an elastic collision, assuming one object is originally stationary, the relative velocity of approach before collision is equal to the relative velocity of separation after collision. This is because the conservation of kinetic energy and the conservation of momentum provide two independent equations that allow us to solve for the final velocities.
When analyzing collisions, it can be easier to deal with elastic collisions as compared to inelastic ones, since, in the latter, some of the kinetic energy is converted into other forms of energy, such as sound or heat, making the equations more complex. Furthermore, to verify the relationship between relative velocities, one would typically use a mathematical approach as opposed to a graphical one because it provides a more precise and quantitative analysis.
To illustrate, if two objects of equal mass undergo an elastic collision, and one is initially at rest, the one that was moving will come to a stop, while the initially stationary one will move with the velocity that the first one had before the collision. This demonstrates that the relative velocity of approach is indeed equal to the relative velocity of separation, satisfying the conditions of an elastic collision.