The Wikipedia page for an O'Neill Cylinder indicates that they would revolve at a rate of around 2.8 degrees per second – at a diameter of 5 miles, that would be a surface speed of about 0.12 miles per second, or ~440 mph.
If the velocity of the surface is 440 mph, then ±40 mph would be about 90–110% of Earth gravity. Not enough to float, but probably enough to require a specialized suspension.
(Edit: Note that the 1g ±10% is a rough estimate, see @TannerSwett's answer for more precise values)
However, are cars on roads actually the most likely transportation method? At 20 miles long and 5 miles in diameter a typical O'Neill cylinder has 300 square miles of area (~775 km$^2$), orwhich is the size of a small county in the USA (or about the size of Bahrain). Roads are mostly wasted space, if you are trying to grow food or house humans. Public transportation is most likely, and trains or trams, connected to a central electric grid, would not pollute the air. And, if you use vehicles on rails, then designing them like roller coasters would 100% resolve any issues with "falling off".