D=v^0 t+1/2 at^2 the 0 is supposed to be really small right next to the v under it

Yes, that's right.

You mean like this: D = v₀ t + 1/2 a t².

That's the formula for the distance covered in ' t ' seconds

by an object that starts out with speed ' v ' and accelerates

with acceleration of ' a '.

An example is the vertical distance traveled by a rock that's

either tossed up from the ground with speed ' v ', or thrown

down from a roof with speed ' v '.

Whenever the formula is used for objects thrown up or down,

the acceleration ' a ' is the acceleration of gravity, on Earth or

wherever the rock-throwing is going on.