After some thoughts, I get that there will be no jerk or change in acceleration ( which I presumed).

Relating the dV/dt=r with the Noyes-Whitney equation, we get a good thing.

Now we define terminal velocity and then use it to equation. That reduces it to one unknown, other than the coefficients which are experimentally determined.

So we get a single equation with dR as the unknown. Solving for this R by transposition and integration.