Chapter 8.2, Problem 53PE

The motion of an object traveling along a straight path is given by $s\left(t\right)=\frac{1}{2}a{t}^2+v_{0}t+s_0,$ where $s\left(t\right)$ is the position relative to the origin at time $t.$ For Exercises 53-54, three observed data points are given. Find the values of $a,v_0,$ and $s_0$ .

$s\left(1\right)=30,s\left(2\right)=54,s\left(3\right)=82$