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Classical Mechanics,motorboat

  • Thread starter prehisto
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  • #1
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Homework Statement


When engine was turned off,boat with mass m was moving with speed v_0.
The force of friction F=-[itex]\alpha[/itex][itex]\nu[/itex]-[itex]\beta[/itex]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?


Homework Equations





The Attempt at a Solution


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

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

Homework Statement





Homework Equations





The Attempt at a Solution


Homework Statement





Homework Equations





The Attempt at a Solution


Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
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Ok,now Im pretty sure that i have to solve DE :
[itex]\int(\frac{dv}{ \alpha v+\beta v^2})[/itex]=[itex]\int dt[/itex]

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?

Please help .
 
  • #3
vela
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Hint: Use
$$a = \frac{dv}{dt} = \frac{dv}{dx}\frac{dx}{dt} = v\frac{dv}{dx}.$$ This is just the chain rule.
 
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  • #4
haruspex
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Ok,now Im pretty sure that i have to solve DE :
[itex]\int(\frac{dv}{ \alpha v+\beta v^2})[/itex]=[itex]\int dt[/itex]

And integration bondaries from v=v_0 to v_0/3 ?
And for other integral of course its from t=0 to t_0
You dropped a minus sign (as well as a factor m). You could fix the sign by changing the v limits to being from v0/3 to v0.
I note that in the OP you gave the force as being ##-\alpha \nu -\beta v^2##. I assume you meant ##-\alpha v -\beta v^2##
 
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