You could always do a gif animation with transparencies and stick it on a plane directly over the ground, but that might get tricky if your ground isn't perfectly flat. Not sure if that would be easy or difficult to do. Also, it would be quite difficult to modify the tire marks if you wanted to change something. Come to think of it, can Maya even import gif's to begin with?

Hmm. Another way would be to make a giant image with the tire marks from start to finish, apply it to a plane, then create another plane with the opacity set to black hole. The "black hole plane" would have to travel over top of your tire track image. You would have to move it to reveal the tire tracks as the vehicle or tire moved along. You would of course, render the tire tracks out, then composite them into your real animation to achieve this effect.

I'm sure there is an easier way to do this though.....