Collision summary
Collision
A collision refers to the interaction between two or more objects, during which they exert forces on each other for a relatively short period. Collisions can occur between particles, such as billiard balls or atoms, or between macroscopic objects, like cars or celestial bodies.
Types of Collisions:

Elastic Collision:
 In an elastic collision, both kinetic energy and momentum are conserved.
 The total kinetic energy before and after the collision remains the same.
 Elastic collisions often occur at the molecular or atomic level.

Inelastic Collision:
 In an inelastic collision, only momentum is conserved, not kinetic energy.
 The total kinetic energy of the system decreases after the collision.
 Inelastic collisions are common in macroscopic objects like cars.
Elastic Collision Equations:

Conservation of Momentum:
 The sum of momenta before the collision is equal to the sum of momenta after the collision.
 For two objects: ${m}_{1}{u}_{1}+{m}_{2}{u}_{2}={m}_{1}{v}_{1}+{m}_{2}{v}_{2}$
 Where is m mass, $u$ is initial velocity, and $v$ is final velocity.

Coefficient of Restitution (e):
 It quantifies the "bounciness" of the collision.
 $e=\frac{\text{relativevelocityaftercollision}}{\text{relativevelocitybeforecollision}}$
 For a perfectly elastic collision, $e=1$, and for a perfectly inelastic collision, $e=0$.
Inelastic Collision Equations:

Conservation of Momentum:
 As in elastic collisions, momentum is conserved in inelastic collisions.
 ${m}_{1}{u}_{1}+{m}_{2}{u}_{2}={m}_{1}{v}_{1}+{m}_{2}{v}_{2}$

Coefficient of Restitution (e):
 In inelastic collisions, 0 < e < 1
 $e$ can be used to determine the degree of deformation or "stickiness" during the collision.
Reallife Applications:
 Road traffic accidents (inelastic collisions).
 Particle collisions in particle accelerators (highenergy physics).
 Billiards and other sports (elastic collisions).