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.
![Tongue](https://www.councilofexmuslims.com/Smileys/custom/tongue.gif)
'Warp'...so somehow the ship alone can affect the space around it and its existing space....o.o