Perhaps you can use the Permalinks.
Admin » Settings » Permalinks
You could set the ‘tag-base’ at the bottom to cars, and chose a structure like %tags%.
I tried this at localhost, and it works.
The problem is, that now all tag-pages have a url with
http://example.com/cars/tagname/
You wrote, that you use lots of tags, and I suppose, they are used in different post-types.
If this is not ok, I would suggest writing a page-template, with
/* Template name: cars page */
and create a page called cars, to display all cars-posts with the requested tag.