$(4$ pts$)$ A ball is thrown straight down from a $600-$ft building and an initial velocity of $-30f\frac{t}{?}$ second. The position function for free$-$falling objects is given by the following equation, where ${}_0$ and $s_0$ are the initial velocity and position, respectively.

$f(t)=-16t^2{v}_{0}t{s}_0$

a$.$ Find the position and velocity functions and label them accordingly.

b$.$ Determine the average velocity on the interval $1,3.$ Be to include appropriate units.

c$.$ Find the instantaneous velocity when $t=3.$ Be to include appropriate units.

d$.$ Find the velocity of the ball when it hits the ground.