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This might be a little too complex for me to understand the answer, But here goes:

1) I have a fictional spacecraft , frictonless and an infinite supply of fuel.

2) It is able to accelerate at 9.8 m/s/s.

3) I want to travel between 2 planets 100 million kilometers apart.

4) I want to accelerate 1/2 way then deccelerate the rest of the way.

I know:

distance = 100,000,000km = 100,000,000,000m

acceleration = 9.8m/s/s

time = ? in seconds

velocity = 9.8*time = ?m/s

I can break the trip in two 50,000,000,000m if I figure the time and max velocity for the acceleration phase, I know it for the deceleration phase.

if I remember right (high school physics was 30 years ago) I would travel

4.9m, ending with a velocity of 9.8m/s after the first second.

9.8m, (total 14.7m), ending with a velocity of 19.6m/s after the second second.

19.6m, (total 34.3m), ending with a velocity of 29.4m/s after the third second.

I know I could use a spread sheet and just keep doubling the distance, adding it to the total distance and add another 9.8m/s to the velocity until I got to 50,000,000,000m, But there must be a formula to figure this out, my question is where can I find the formula.

Thanks

Rich