A boat of mass $\displaystyle m$ is traveling with velocity $\displaystyle v_0$. At $\displaystyle t=0$ the power is shut off. Assuming water resistance is proportional to $\displaystyle v^n$, where $\displaystyle n$ is a constant and $\displaystyle v$ is the instantaneous velocity, find $\displaystyle v$ as a function of the distance traveled.