Problem regarding sampling of a nurbs curve

I have the following problem regarding sampling of a nurbs curve. I have not much of an idea where to start. For now I am interested in how one could approach this-- Any hints?
Many Thanks!!

Let’s image a car moving along nurbs curve road. The car can move at different speeds but is very susceptible to forces acting on the car.

(speed) The first force is due to the speed the car is moving: at 100mph the windresistance is high enough that the windshild cracks

(acceleration) due to the bad construction of the car, it will break when the driver takes a tight turn without slowing down

(jolt) due to a almost broken gaspedal the driver can not push the pedal in a hard, (on/off) way but has to carefully and slowy lift or lower his foot.

Since years of experience with his bad car the driver knows just how to drive as fast as possible, right at the limit of breakage.

Overlooking the nurbs-curve road, where will the car be at time T?