## Calculus, 10th Edition (Anton)

$$s(t) = 2t^{3/2}-15$$
Given $v(t) =3\sqrt{t}$ , $s(4)=1$ Since \begin{align*} s'(t)&=v(t)\\ s(t)&=\int v(t)dt\\ &=\int3\sqrt{t} dt\\ &= 2t^{3/2}+c \end{align*} Since $s(4)=1$, then $c=-15$, and $$s(t) = 2t^{3/2}-15$$