I'm with Dave. The 70-200 lens is FAR more versatile than people give it credit for.
If you like this style of auto photo, get a wide angle lens. As Dave said, you're 18-35 will have no problem creating this effect.
If you like your auto photos to look like regular auto proportions, get a lens with a longer focal length. This was taken at 125mm with a 70-200 zoom lens.
If you want a prime lens and intend to take photos of cars, i'd get 100mm lens. Because you need to be a fair distance away from the car when shooting at 100mm or more, a fair compromise is the 60-70mm focal range. This is at 65mm taken with a 24-70 zoom lens.
But if you look close, you'll see that not all of the vehicle is in focus. That's because shooting in dawn or dusk lighting will require a low F value. (unless your camera has good high ISO performance or you're using a tripod) Couple that with a shorter focal length and you'll end up with a shallow depth of field causing some of the subject to be OOF. If i were you, i'd shoot at the long end of that 18-55 until you find a legitimate need for a new lens.
To round out Dave's answer about why you would you get the 35 1.8.... as others have said, you may want it because it's a fast lens, which means you can get good performance in low light. But when using that super low F value in low light, it comes at the expense of DOF. In my opinion, your money would be better spent on a sturdy tripod than a fast prime lens that's within the focal range of your existing lens. I also think that short focal length primes make for great artistic photos by using that shallow DOF. I also argue that most people prefer more DOF when shooting cars.