Elastic collision and its derivation?

The elastic collision formula comprises two parts, namely elastic collision formula for kinetic energy and elastic collision for momentum. 

However, Follow the Table Below to Understand What each Component in the Equation Signifies –

Therefore, the formula for elastic collision kinetic energy is – 

On the other hand, the elastic collision derivation for momentum is – 

m1 u1 + m2 u2 = m1 v1 + m2 v2

A fundamental way to make sure whether a collision is elastic or inelastic is by equating their total kinetic energy. In case it remains the same as before and after the said collision, you can label it as elastic collision. Contrarily, a shift in the total kinetic energy suggests that the category of collision is inelastic. 

However, the energy loss for inelastic collision usually dissipates into sound and heat energy. It helps in maintaining the balance of energy before and after.