Question

What does d=1/2gt^2 solve?

Answer 1

Physics is a bit difficult, I try to explain.

You know that the acceleration formula (to find the distance) is d=1/2at^2, when you have no initial distance and no initial speed.

d=1/2gt^2 is the formula for the Free Fall (the only acceleration that acts on the object is the Gravity Acceleration) and since we consider the y-axis positive when oriented up, it solves from ground to peak (object thrown upward).

The formula when the object goes downwards is d=v0t - 1/2gt^2

Hope it's clear, in case leave a comment.