You drop a rock down a well that is 31 m deep. How long does it take the rock to hit the bottom of the well?

In order to keep this problem simple, we can assume that the acceleration

of gravity is constant over the distances involved ... 9.8 m/s².

(When you get super-technical about it, once you go below the surface

of the Earth, gravity actually decreases the deeper you go.)

A useful formula here is:

Distance in free-fall = (1/2) (gravity) (time) ²

31 m = (1/2) (9.8 m/s²) (time) ²

Divide each side

by 4.9 m/s² : 31 m / 4.9 m/s² = time²

31/4.9 s² = time²

Square root each side: time = √ (31/4.9) s

= 2.52 sec (rounded)