...and goes up at least once without the aid of a lifthill or an engine...then it's a coaster.
Therefore Dragster wouldn't be a coaster. Somethings wrong about that.
Whats the precise definition of rollercoaster?
We could even argue about this one. Because I Think its a bit too unspecific.
But that discussion is a neverending story and its only relevant for counting and not for having fun on a ride.