Re: Ship accelerates in space

It's quite simple really.  The only reason a space ship (or any other 
object) will accelerate (where "accelerate" means to change velocity, 
either in magnitude or direction) is if a force is applied to the 
spaceship.

When you cut off the engine of the ship, there is no longer a force 
being applied to the spaceship, so it "coasts" along at a constant 
speed.

In essense, the situation you are describing is encompassed in 
Newton's First Law:  "An object moving at constant velocity (including 
zero velocity) will remain at constant velocity unless acted upon by a 
force."  In other words, you need to apply a force to accelerate 
anything...