How much longer does it take to fall double the distance?

time-to-splat.md

Time to fall double distance

$a' = 0$

$v' = a$, $v_0 = 0$, so $v(t) = at$

$d' = v$, $d_0 = 0$, so $d(t) = \frac{at^2}{2}$

rearrange $t$ to subject: $t(d) = \sqrt\frac{2d}{a}$

Time for double distance is $t(2d) = \sqrt\frac{2(2d)}{a} = \sqrt{2}\sqrt\frac{2d}{a} = \sqrt{2}\cdot t(d)$