A constant 1g acceleration is a great idea, it takes care of any physiological issues that might result from prolonged exposure to a weightless state. It's long been a staple in science fiction stories. But it has its problems, too.

First, it requires throttling back on the engine. The thrust of a rocket is the force which causes it to accelerate, remember our old friend F = ma, from Sir Isaac himself? Solving for the acceleration: a = F/m, but as the ship's engines fire, m is constantly decreasing as fuel is consumed, so to keep the accelleration constant, the force (engine thrust) must be reduced. In other words, you have to throttle back the engineand reduce the thrust as the ship gets lighter.

We can be pretty sure our engine will be designed to run as efficiently as possible, and it will probably run best (as do all engines) at one particular power level. It may be possible to alter throttle settings, but we can expect it won't be as efficient at thrust levels outside its optimum range. Something as complex and sophisticated as a starship powerplant, probably a highly complex and tuned fusion rocket, will not be possible to build if we expect optimum efficiency at all power levels.

But even if that were not a problem, there is another constraint on our 1-G requirement. One G is an accelleration of 9.8 meters per second per second. The formula for velocity v at an acceleration of a after a time t is very simple: v = at. We calculated earlier that a reasonable final velocity for a fusion rocket would probably be around 0.1 c, or 3 x 10**7 m/s. To get up to this speed would then require our 1-G engine to operate for a time t = (3 x 10**7)/9.8 seconds,or roughly,five weeks.

So by the time you ran out of fuel, a month into the trip, you'd still have 40 years of free fall ahead of you before you got to the nearest star.