Suppose two objects of different mass, A and B, collide with each other. Now, during the time of collision, they both apply forces on each other according to Newton's 3rd law. Therefore, their accelerations won't be equal.
Here, my confusion is that, while they are colliding, they are both touching each other. Hence, the kinetic properties of one object must coincide with those of the other one as well (since you cannot keep two objects with different accelerations and velocities in touch for a non-zero amount of time). Therefore, their acceleration must be equal to each other at any instant. Now, this seems to contradict Newton's 3rd law. Where is the problem?
PS: I am talking about elastic collisions.