Question

what are the equations for the conservation of momentum for Inelastic and elastic collisions?

Answer 1

A collision is elastic or not depending on whether KE is conserved or not, as we've seen in a few of your questions now.

That being the case, Conservation of Momentum is unchanged whether KE is conserved or not.

Answer 2

How do I find the change in Kinetic energy

Answer 3

If a body of mass m has velocity v before an event and velocity v' after the event, then the change in KE is
\[ KE_{after} - KE_{before} \]
\[ = \frac{1}{2}mv'^2 - \frac{1}{2}mv^2 \]
\[ = \frac{1}{2}m (v'^2 - v^2) \]