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## Homework Statement

A 1000 kg boat is traveling at 90 km/h (25 m/s) when the its engine is shut off. The magnitude of the frictional force

*f*

_{k}is proportional to the speed

*v*of the boat:

*f*

_{k}= 70

*v*; where

*v*is in meters per second and

*f*

_{k}is in Newtons. Find the time required for the boat to slow down to 45 km/h (12.5 m/s). The answer is suppose to be 9.9 seconds, but I have yet to figure out how to approach that answer. Feel free to help me using calculus if needed.

## Homework Equations

F

_{net}= m

*a*

*f*

_{k}= [tex]\mu[/tex]

_{k}F

_{N}= 70

*v*

## The Attempt at a Solution

I first tried to write down all forces acting on the boat prior to the engine shutting down:

F

_{Engine}-

*f*

_{k}= F

_{net}

m

*a*

_{Engine}- 70

*v*= m

*a*

_{1}

Then I wrote down the equation for when the engine did shut down:

F

_{Engine}-

*f*

_{k}= F

_{net}

m*0 - 70

*v*= m*-

*a*

_{2}

But now I'm stuck as to where to go next.

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