If you want to use "rush" you need a preposition of movement. "The car rushed down the hill." "The car rushed along the road." Or use "rush" as a phrasal verb: "The car rushed along at 120 mph." "The car rushed off." But I don't think it's common to use "rush".
If you search for "the car rushed" and then follow the "in context" link you will find examples. Once you have sifted examples that are actually this construction from the rest, you will find that some are by native English speakers.
The Atlantic-18 Nov 2013
(Quoting CBS News from 1963) The President, cradled in his arms of his wife, Mrs. Kennedy, was carried to an ambulance and the car rushed to Parkland Hospital outside ... WOWT-21 Aug 2014
As the car rushed toward the pump, one man tells us he barely pulled his sister out of harm's way. Telegraph.co.uk-1 Oct 2012
"Suddenly there were lots of policemen in plain clothes. They blocked the two in a side street and then the car rushed off."