Tjeerd, a good friend of mine stood in a field with a slight tele-lens (85mm) and the following values: ISO400, f/18 and 1/125 shutter, and a Minolta Dynax 7D camera. He moved the lens with the car whilst taking the photograph. However, I also used a little photoshop to make the blurring in the picture a little more pronounced.
Since then I have bought better equipment, and I can quite reliably shoot pretty good car moving pictures… such as this one: no Photoshopping involved, Canon EOS 60D, 75mm lens, ISO 800, f/4, 1/800 (which is why the car is sharp), moving with the car.
Or this Mustang… not moving as fast (it is in the pit lane). Both of these were taken during the European EVent 2012 at Spa Francorchamps circuit.