Let's see here..... another way to do this would be to create many, many very small planes and place them right next to each other in the path of the tire(s). You would have to animate the transparency or visibility for each face so that the tracks seem to appear as the tire rolls over them.

I believe you could also just create a big long plane, apply your tracks image to it, then map a ramp to the transparency or something and have it so the white=transparency and black=zero transparency. You would then animate the little bar things on the actual ramp so that your transparency follows the tire according to your animation. I'm not entirely sure if you could really do this since I haven't done this particular thing before, but it should work.