## Calculus, 10th Edition (Anton)

$$s(t) = 16t^2+20$$
Given $v(t) =32t$, $s(0)=20$ Since \begin{align*} s'(t)&=v(t)\\ s(t)&=\int v(t)dt\\ &=\int 32t dt\\ &=16t^2+c \end{align*} Since $s(0)=20$, then $c=20$, and $$s(t) = 16t^2+20$$