A ripe acorn falls down from a branch with an initial velocity v0 = 0. The acorn's vertical displacement until it hits the ground (neglecting the effects of air) could be derived using

s = 9.81t²

Explanation:

The equation of the vertical displacement of the unicorn at any time t, can be derived using the equation of linear motion

s = Vo. t + 0.5at²

where s is the displacement,

Vo is the initial velocity,

t the change in time from t = 0

a is the acceleration which for bodies falling under gravity without air resistance is 9.81 m/s²

So the equation simplifies to

s = 4.905t²