On the moon, all free$-$fall distance functions are of the form $s(t)=0\mathrm{.}81t^2,$ where $t$ is in seconds and $s$ is in meters. An object is dropped from a height of $350$ meters above the moon. After $8$ sec $,$ consider parts $($a$)$ through $($d$)$ below.

a$)$ How far has the object fallen?

b$)$ How fast is it traveling?

c$)$ What is its acceleration?

d$)$ Explain the meaning of the second derivative of this free$-$fall function.

a$)$ The object has fallen $$ m$.$

$($Type an integer or decimal rounded to two decimal places as needed.$)$