I just derived a useful equation for the first time. I feel so good right now.

just a heads up, this is probably rambling a bit, but I just want to share my experience.

Now then, a couple of minutes ago I was attempting to find the maximum horizontal velocity of bullet fired from a Glock (disregarding air resistance, curvature of the Earth, etc.) in response to another comment on Reddit (see here). I used my AP Physics 1 knowledge of kinematics and the equations [;v_f = v_i + a * t;] and [;d = v_i * t + (1/2)a*t^2;]. I got an answer, but I wanted to see if I could find a simple formula to find the distance given only the inital velocity. The time is the same in both equations, as is [;v_i;], and [;v_f;] is zero, so it should be possible.

After playing around with the equations, I was able to determine that [;$d = v_i² /a $;]. I've seen a ton of derivations for all sorts of things online and in textbooks, and they all seem really obvious when I read them, but this was the first time I was really able to derive one myself. It's such a good feeling knowing that discovered this all by myself.

It's kind of annoying though because this equation would have been so useful to have on my AP Physics 1 exam and my teacher never bothered to give us this equation to us, but I digress.

I'm just feeling really good about myself right now.

I can also post my derivation if anyone is interested.