There should be no acceleration during warp, because the ship stays still in space: it's the space around the ship that is moved around the universe... or something.
Ok, otherwise I would've asked why doesn't the ship crash into stars/planets/comets etc that are in front of it, that is in the path it travels, assuming ship motion only occurs in one direction.
'Warp'...so somehow the ship alone can affect the space around it and its existing space....o.o