Originally posted by sonhouse
So this genius kid figures out a few what now is sci fi, a small anti-matter power source, and a kind of propulsion unit that would accelerate everything at the same rate so you can do accel at a million G's without getting squashed.
So his maiden voyage is to the moon, we call it 384,000 Km or 240,000 miles away take your pick.
The question is, how long ...[text shortened]... land on the moon at 1 million G's. What is his average velocity and what is the peak velocity?
Accel = A
Velocity = Ax
Dist = 1/2*Ax^2
A = 1 000 000 * G
G = 9.8 m/s^s
Assuming positive acceleration for the first half of the journey, and negative acceleration for the second half.
Dist = (Dist to moon)/2 = 192 000 000 m
192 000 000 = 1/2 * A * x2
x ~= 6.26s
Max Velocity = A*x = 9 800 000 m/s^2 * 6.26s = 61 344 926 m/s
Total time = 2x = 12.52s
Ave velocity = 384 000 000m / 12.52s = 30 672 563 m/s
I haven't looked at or thought about basic calculus in quite some time. Sorry if I solved your problem before others had a chance.