This is good! Although I'd also say that initial velocity doesn't quite cover what I was talking about in the post -- even anticipation arguably can start from 0 velocity, accelerate backwards, decelerate, then accelerate in the opposite direction. Imo, any sudden change in velocity should by default be avoided (there are always valid uses where breaking that expectation is good, but I'd want it smooth by default.)

That could possibly be done by incrementally changing force to move it back first, then forward, or to model this as a PD controller following an input with some baked in reversal before moving forward. That can still be closed-form (state response to a known input will be; Laplace transforms can help there), but still would need a bit of effort to model and tune to look right.