Need to derive the distance formula from the acceleration due to gravity

[Icedfire01]

Pretty much like the title says. I'm having a hard time finding where the formula: d=1/2gt^2 comes from. Any help would be greatly appreciated.

 

[robphy]

What facts or definitions do you have to start with? (Are you taking an algebra-based or calculus-based course?)
[By the way, post your question in only one thread.]

 

[amcavoy]

Start with acceleration, "a." You know that the second derivative of "a" is "s'', where "s" is the position. Integrate twice and adjust for the constants.

∫a dt = at+v₀ = v

∫v dt = .5at²+v₀t+s₀ = s