I don't think you need interpolated coords. Build the track in such a way that the sides extrude like so ..
View from behind the car
ccc = car chassis
w = wheel
* = Track ( slightly wider than wheel base )
ccc
* wcccw *
*********
Your car should consist of a visible entity and 2x pivots representing the front and rear axles, set to sliding collisions . The 2 x collision pivots would have to be constrained so that they stay within the length of the wheelbase ( same way as verlet ) ... a simple spring system will do the trick here.
When you accelerate apply the acceleration to the rear pivot in the direction of the front pivot and every frame position the visible entity in the center of the 2 pivots, pointing at the front one. Obviously gravity would also need to apply to both pivots.
Due to the constraining the vehicle will turn automatically as the front pivot hits the side of the track.
Probably a bit long winded but just thinging out load here. I'm pretty sure it would work.
What you making .. skalextrix ( spelling??? ) ?
Stevie