Suppose we have two balls, $A$ and $B$, of radius $1$ with equal mass. Ball $B$ is initially at (center is at) two on the $x$-axis, i.e. $(2,0,0)$, and has velocity $0$. Ball $A$ is initially at (center is at) some point on the $x$-axis to the left of ball $B$ (not touching ofc) and is moving right with speed $s > 0$. Some time later the balls collide, and following the collision, ball $A$ is now stationary and ball $B$ is moving right with speed $s$.
If an impulse model is used then the collision between $A$ and $B$ is treated as occurring instantly and following the collision the center of ball $A$ is at the origin.
If the collision is modeled using forces, will the center of ball $A$ end up being exactly at the origin? Or might ball $A$ end up with center at $(\epsilon, 0, 0)$ for some small nonzero $\epsilon$, or even at some point $c$ not on the $x$-axis with $||c||$ small but not zero? If the center of ball $A$ does not end up exactly at the origin, what might be some of the major properties that determine where it does end up? What about if such a collision occurs in reality?
From my limited understanding, during the collision there is temporary deformation and spring-like forces at work. For some small proper interval of time ball $A$ (center of mass) decelerates while ball $B$ (center of mass) accelerates, but even if $A$ ends up stationary it's not clear to me that it's center will end up where it was when the collision began.
Any help or information is very much appreciated. Thank you for your time and have a great day.