Hi,
There is nothing difficult here in terms of technic and car control/ai. Tho, obviously, the idea is real nice and extremly well executed.
I would go for physics based control and apply a constant force to the car, that's all, then other cars and props are colliders and triggers, and the physics engine will do the rest, slowing down and crashing car if hit its props and cars.
As for the logic to give penalties to speed an all, it's simply applied to the force amount you give to the car, to slow down, simply add less force.
you can also control the car velocity directly, you can see an example of velocity control ( to max out speed for example) in this break out sample:
https://hutonggames.fogbugz.com/default.asp?W936the ball is moved with force and it's velocity is monitored and maxed out. that would be a good base to use for this car behavior, at least to get inspired on how to control it.
bye,
Jean