# Classical Mechanics,motorboat

prehisto

## Homework Statement

When engine was turned off,boat with mass m was moving with speed v_0.
The force of friction F=-$\alpha$$\nu$-$\beta$v^2.
How long it would take to drop speed of boat 3 times?
Find the distance which the boat will travel in this time?

## The Attempt at a Solution

I think i should try to solve differental equation in form of
m$\dot{v_0}$=-$\alpha$$\nu$-$\beta$v^2

But I realy dont know what to do next,could someone,please help me with some steps or tips?

## The Attempt at a Solution

prehisto
Ok,now Im pretty sure that i have to solve DE :
$\int(\frac{dv}{ \alpha v+\beta v^2})$=$\int dt$

And integration bondaries from v=v_0 to v_0/3 ?
And for other intergral offcourse its fromt=0 to t_0

Either way, how can I find the distance?

Staff Emeritus
Homework Helper
Hint: Use
$$a = \frac{dv}{dt} = \frac{dv}{dx}\frac{dx}{dt} = v\frac{dv}{dx}.$$ This is just the chain rule.

• 1 person
$\int(\frac{dv}{ \alpha v+\beta v^2})$=$\int dt$
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