Question

If an object starting from rest falls 5.7 seconds how far does it fall

Answer 1

Kinematic question!
Start with your knowns!

$t = 5.7s \\ v0 = 0 \frac{m}{s} \\ a = - 9.8 \frac{m}{ {s}^{2} }$
we want to find x!

the only kineamtic that works with this info is the third!
$x = v0 \times t + \frac{1}{2} \times a \times {t}^{2}$
so we plug in our values and get
$x = 0 + \frac{1}{2} \times ( - 9.8 \frac{m}{ {s}^{2} } ) \times ( {(5.7s)}^{2} )$
this'll equal out to -159.2 meters.

our units equal out, so we know our answer is correct!