Chapter 4.3, Problem 85E

Distance. For a freely falling object,

$\begin{array}{l}a\left(t\right)=-32\text{ft/sec}?,\\ v\left(0\right)=\text{intial velocity}=v_0\left(\text{in ft/sec}\right),\text{and }\\ s\left(0\right)=\text{intial height}=s_0\left(\text{in ft}\right)\end{array}$.

Find a general expression for $s\left(t\right)$ in terms of $v_0\text{ and }{s}_0$.

$s\left(t\right)=-16t^2+v_{0}t+s_0$