when it comes to shooting motor sports panning is almost your only option. When I say panning I am talking about following the subject with your camera as it moves. The trick to this is using a slow shutter speed. depending on your lenses focal length you may want to shot from 1/40th to 1/125th of a second.
Gordon, The editor of Camera Labs has a great tutorial explaining furhter how do do this and you can find it on his other site here:
P.S. To get the same panning motion from the front of a car you will need a zoom lens. as the car comes closer zoom out to keep it in same spot of the frame and try your best to keep it the same size in the frame.
Please let me know if you have any questions.