Wondering where the distance formula from acceleration due to gravity comes from

[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.

 

[misogynisticfeminist]

If a=g, then integrate twice with respect to time !

 

[quantumdude]

That's almost right. When you integrate twice you pick up two arbitrary constants of integration. To really derive the formula you would have to solve the following initial value problem:

$$\frac{d^2y}{dt^2}=-g$$

$$y(0)=0$$

$$y'(0)=0$$.