Newton mechanics? addition of collision velocities is really related to Energy additions?

Question

do 2 equal masses moving at different velocities,when they collide is collison velocity equal or greater than the sum of inertial velocity? can this be calculated without relativity special?

Answer 1

if both the objects are moving they will pocess some kinetic energy, which is proportional to the square of their respective velocities (K.E=mv^2/2).
So, if you are adding collision velocities, you are adding the kinetic energies.

Answer 2

Newton's second law leads to the "conservation of momentum" and "conservation of energy"

When two masses are experiencing collision momentum must be conserved, giving out the right predictions for their velocities before and after the collision and giving out the right transformations of energy to keep it conserved as well.

We classify collisions as either elastic or inelastic depending on whether the collision conserves kinetic energy or not. Collisions between hard objects which rebound off each other are completely elastic. Soft objects which stick together after the collision are termed completely inelastic. Although it was not known in Newton's time, conservation of energy is no less fundamental than conservation of momentum. However, since energy can appear in many different forms, some of which are difficult to observe, it took many years and experiments in many branches of physics and chemistry to prove that energy (as distinguished from kinetic energy, the energy associated with motion) is also conserved in all collisions. In inelastic collisions some of the kinetic energy is absorbed into deforming the colliding objects, some into sticking them together, and the remainder appears as heat.