Assume that you have a conventional automobile, but with a very very powerful engine- that can continue to produce enough power to accelerate even when it is travelling at a very high velocity and with huge frictional losses and air resistance.
Now that we got the weakness of the engine out of the way, let us assume that there is a perfectly 'smooth' and 'straight' road constructed all the way around the moon. By smooth, I mean smooth as a racetrack and not smooth like a skating rink, ie., the road has only microscopic roughness that produces friction. It does not have any macroscopic bumps, etc.
Having defined the operating conditions (which, I hope, is what the OP asked), let us examine how the car accelerates. The engine exerts a torque on the wheels, which is translated to motion if there is sufficient friction between the wheel and the road. As we all know, the limiting friction that the road can exert on the car, accelerating it depends on the amount of normal or contact force between the road and the wheels of the car. If the normal force is large, a large amount of friction is available and the car, if it has a powerful enough engine, can accelerate by a large amount. However, if the normal force becomes zero, there can be no frictional force. The normal force is provided by the force of gravity on your car.
Let us make an assumption about our car. 461
Let us assume that it has good aerodynamics for speeding, ie., fast moving air won't cause it to become airborne. When we start to zoom around the moon in our hypothetical car, initially, we will accelerate normally (as normal as you can expect in the moon). Granted, the maximum acceleration will be much lower than the acceleration you can expect on Earth, but still you can accelerate. However, as you keep increasing your speed, something strange happens. You will find that the maximum acceleration you can maintain without skidding on the road keeps reducing. This is because, as you keep increasing your speed, the centrifugal force due to your motion around the moon starts coming into picture, and it acts against the gravitational force, effectively reducing the amount of normal force on the tyres of the car, lowering your acceleration. This will continue, until you slowly reach the orbital speed on the surface of the moon, where the gravitational force is completely balanced by the centrifugal force due to your motion. At this point, your car engine becomes useless (even if it has plenty of spare power), as your car is effectively floating around now. Thus, the orbital speed of the moon is the largest speed that you can achieve when travelling in a conventional automobile, although there are plenty of easier ways to travel at this speed. 461