Question

When two objects moving with velocities v1 and v2 and of masses m1 and m2 respectively towards each other collide with each other and get sticked.Can we say that this happened because in order to conserve the linear momentum,theit initial velocities are equal to their velocities after the collision i.e. their final velocities?

Answer 1

we apply the principle of conservation of linear momentum.  We cannot apply the principle of conservation of mechanical energy as, there is some loss of energy in deformation or sound energy.

let the two bodies get stuck to each other and travel with a speed v.  They travel together with the same speed.

     m1 v1 + m2 v2 = (m1 + m2) v
       v = (m1 v1 + m2 v2) / (m1 + m2) 

Suppose m1 = m2,  then
        v = (v1 + v2)/2

so their final velocity can be equal to initial velocity only if  v1 = v2. Then there is effectively no collision. 

Thus, after collision, the initial velocities cannot be equal to final velocities.  But an exchange of velocities can happen.  But then the bodies do not stick to each other.