Divide and conquer.
Slice the track up into 'sections'(every 30 foot for example), find the centre, of each section, give each section a radius which covers the section.
Give your car a radius, double it to be safe when moving at speed.
Use circle to circle (fast, can be done in one line) to select which section (or sections) are under the car. (Cars are not planes, the chances are they are either on the same one, the next or previous on the list of circles, so only check these)
Use this result to select what sections to examine in more detail. At this stage, use a simplified (not used for onscreen rendering as Gernot suggested) track section polygon to check if wheel(s) off track.
There are other methods, quadtrees for example to partition space etc... but this may be OTT for a simple racer collision but may improve rendering speed via culling selection.