To keep the car sharp but motion blur the background, you can either shoot stationary and pan with the subject, or shoot from another vehicle moving at the same speed. Try different shutter speeds, depending on how fast the car is moving and how far it is from you (how fast it moves across the frame). The closer it is to you or the faster it is going, the faster the shutter you want. For most rolling shots reasonably large in the frame, shutter is around 1/30", but your best results are likely to be anywhere from 1/4" to 1/60". I see a lot of ad shots taken from cameras mounted low on a chase car, using a short lens and a shutter speed on the longer end of that spectrum.
Keep in mind that although the background will be blurred, you want it to be recognizable, so too long a shutter is no good. Also, many photographers wrongly figure that since the background is blurred, it doesn't matter so much, but the good ones know that the background is still important, even in a motion blur shot. So pay attention to your surroundings and shoot it when the background sets off or frames the car nicely.
Here's a tutorial:
http://digital-photography-school.co...ur-photography