While we're on the subject of Dwarven Top Gear, let's examine the feasibility of adamantine cars.
This subject was touched upon a earlier in this thread, but never really explored as it was deemed that the car would be so light it would simply float away. As we know, adamantine has about the same density as cork (around 200kg/m^3, if memory serves). To put this into perspective, the density of carbon fiber is 1780kg/m^3. This would make the prospect of keeping the car on the road very daunting indeed, as you could not allow for any lift whatsoever. But in addy's favor, here's another morsel: the density of fibreglass is around 500kg/m^3. Now that's reasonably near addy's density, so a car designed like, say, an Ariel Atom or a Caterham should do fine. This is because almost all of the weight is the engine; there's very little in the way of bodywork. But at the same time, this rules out addy cars as everyday vehicles.
The only real solution is to do what Pagani did to make carbotanium, and weave the adamantine with another, heavier material (incidentally, other people in this thread have suggested the same thing). This would be possible with today's tech, but it would be extremely cost-prohibitive. So you wouldn't expect to see very many baby blue Accords and Altimas running around.
Another, more research-intensive solution would be to design an entirely new type of car from the ground-up. As we've established, adamantine can be sharpened to a point so fine that it can casually cut through air. So, what you could do is have a car which isn't affect by either lift or downforce. This is entirely implausible if only because it would never, EVER be allowed on the road. Why wouldn't be on the road? Because it's too dwarven.
The final --and by far the largest-- nail in the coffin for the addy car is safety. As we've established over the course of this thread, adamantine has the potential to chip apart into super sharp shards if struck with another piece of adamantine. And it's also been established that adamantine would have no "cushoning" effect in an impact. So imagine two cars going let's say 50 mph. One is going north, the other is going south. South swerves to hit a duck, and accidentally hits north. As most of you know, cars today are built with crumplezones designed to direct energy away from the cabin during a collision.
An adamantine car can't to that. If you get into a crash, you will be killed. End of story.
I apologize for the wall of text, so here's the tl;dr version: An addy car would be expensive to build, expensive to design, ludicrously unsafe by any standard, and far too expensive to research.