This is simply a thought experiment. Say that I had a space craft capable of constantly accelerating or decelerating at a rate of 1g to 3g. I want to hit a target 20 light years away. How would I know where along the way to turn the ship around if I wanted to end at my destination decelerating at a rate of 3g. I have worked out that with a constant rate of acceleration (for example 1g) I would have to begin decelerating at 10 Lr. The catch here is that I want to change the rate of acceleration or deceleration gradually along the trip to eventually simulate 3g aboard the ship. I've been building a dynamically modeled system to answer my question but there must be an easier way. I think I have to integrate my rate of acceleration over a set of points, but its been awhile since I took calculus. Any takers?