Question

Why does d = 1/2gt^2? Is there some intuitive explanation behind, or is this only the result of simplification of equated formulas?

Answer 1

I ask because things like the formula for the number of diagonals in a polygon have a great explanation, so I am wondering if this does. http://www.artofproblemsolving.com/Videos/external.php?video_id=58

Answer 2

I think I found it: "Now the trickier part. How to find distance traveled when velocity is steadily increasing. If a mass starts falling from rest, then after a time t, its speed is v_f=gt. Now imagine that it had gone the whole distance at that speed. Then the distance d is d = v_f t = gt^2. That's clearly an overestimate because since it starts with speed zero, its average speed is v_a = 1/2gt. So it makes sense that the distance traveled in time t is d = v_a t = 1/2gt^2. This isn't really a proof, but hopefully, I've made it at least believable."