# Thread: Motion with resistance problem

1. ## Motion with resistance problem

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.

2. Originally Posted by jmedsy
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.
You have (force=mass x acceleration):

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

where $\displaystyle v(0)=v_0$

CB

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