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I think Dan has the answer -- I'll add one more obvious item.
Very simply KE is dissipated until both are moving at the same speed
whether it's thru gross inelasticity (one ball is sticky putty) or it's
plastic (or not) deformation of a steel railroad car coupling, or
whether it's completed slowly or quickly.
The "maths" is so transparent I don't see anything more to it.
Because it's done so slowly and even then w/ a resulting jerk, I suspect
there isn't a "soft" dissipater.
Here's a page that may answer the soft dissipation question.
"In contrast[,] the Janney couplers (see below) encourage violent
encounters in order to engage the coupling fully."