Twisted science

This post I made earlier was wrong when I did it and I am not sure why I even posted it, I guess I am just lazy. Thanks to XKCD for some reference and something else to think about. My Calculus teacher always told me to write out all the steps and now I know why, sometimes you don't do what you think you are doing.

d=1/2 a t^2
thus 
2d = a * t^2
thus
2d/a = t^2

It is a silly thing, but what I was describing works out the same way as they are defined circularly. However I am certain that XKCD is correct, ( v = sqrt(20h ) where a is in m/s and is 9.8, or in "King of England units" 32 fps/s, I just haven't figured out why I have decided to do things this way. I am horribly wrong on this one . I was having too much fun with laTex / SpeedCrunchand when I get it all sorted out I will do <strike> to show where I screwed up. It is always interesting, for me, to wander into stupidity as it gives me a chance to look at things in new ways and once in a while it gets results, rarely, but it is always fun. I still have not figured out what was motivating me for all this and when I understand it well enough to determine what I got tangled in, I will be happy again. This may be the twisty little answer I was looking for.

ADDED: I suppose it is confusing for me to put up bad equations, but the problem is that I get too many things going at once and the mind can be a real mess when you try to multi-task. I never talk on the phone or text when I drive. In this case I was editing my personal wiki in the section of Physics and forced harmonic motion and chaos as it relates to multiple pendulums, using SpeedCrunch to verify something unrelated to what I was blogging about and blogging about what I was doing, reading wikipedia about pendulums and chaos, playing with laTex equations, learning laTex syntax and history from the web, experimenting with Python in blender, and responding to emails about an xsane issue from a customer.

Looking back ( to help me avoid such things in the future ) I see that it all stems from dividing one side by "a" and multiplying the other by "a". I am glad I wasn't in a heated battle with the Borg as I would be dead now.

v=at
average v = v/2
1/2 a t^2 = d
d/v = t
(1/2 a t^2)/(1/2 a t) =t
t = a * sqrt(1/a * 2 * d) = sqrt( 2 * a * d )

So there it is without trying to balance three plates on my nose while texting about a new version of the "Cube" engine. When I do laTex again I will add the changes. The stupid thing is that I knew it was wrong when I did it and decided to do it anyway. I will have to check my wiki and see how I entered the equations there. I will be more careful in the future as it is embarrassing to make such a silly mistake.