Answer
a. $ 16\ ft/sec$, $ -48\ ft/sec$
b. $2.5\ sec$, $105\ ft$
Work Step by Step
a. We can calculate the instantaneous velocity as the instantaneous rate of change from the height formula as
$v(t)=s'(t)=lim_{h\to0}\frac{s(t+h)-s(t)}{h}=lim_{h\to0}\frac{-16(t+h)^2+80(t+h)+5-(-16t^2+80t+5)}{h}=lim_{h\to0}\frac{-32ht-16h^2+80h}{h}=lim_{h\to0}(-32t-16h+80)=-32t+80$.
Thus we have
$v(2)=-32(2)+80=16\ ft/sec$
and
$v(4)=-32(4)+80=-48\ ft/sec$
b. Let $v(t)=0$. We have $t=\frac{80}{32}=2.5\ sec$ and
$s(2.5)=-16(2.5)^2+80(2.5)+5=105\ ft$
