1. Motion with resistance problem

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

2. Originally Posted by jmedsy
A boat of mass $m$ is traveling with velocity $v_0$. At $t=0$ the power is shut off. Assuming water resistance is proportional to $v^n$, where $n$ is a constant and $v$ is the instantaneous velocity, find $v$ as a function of the distance traveled.
You have (force=mass x acceleration):

$m \frac{dv}{dt}=-kv^n$

where $v(0)=v_0$

CB

3. This problem is in a section involving the spring-dash-pot system. I'm still unable to relate the problems.