Friction proportional to velovity. Help please

[ssm11s]

1. A 1000kg boat is traveling across a lake when its engine is shut off. The magnitude of the frictional force between the water and the boat is proportional to the boat's speed (proportionality constant is 70) . Find the time it takes the boat to slow to one half its speed when the engine was shut off.



2. We have to solve this problem using Newton's second law: F=ma



3. I thought about this problem for over a week now, and I really need all the help I can get!

 

[lanedance]

first write the force as a constant times velocity, then equate with the acceleration equation you gave...

then do you know how to integrate?

 

[ssm11s]

yes i know how to integrate but I am not quiet sure how to develop the integration. what should the variable be ?

 

[marymclellan]

what did you get for the sum of your forces

 

[marymclellan]

do you think there is an f app? or just friction force moving the boat. like a car on a road? i think it would be the same situation, do you?

 

[marymclellan]

i think we use vfinal = v initial + at. as v/2= v + at. and a = (sum of forces divided by mass). i also think I am in your class.

 

[ssm11s]

yeah i think there exists only a friction force. so the sum of forces would be : -f=ma

but the problem is the acceleration is not constant because the f is not constant

 

[marymclellan]

so t = (v/2 + v)(1/a). and a = the 1st integral of v. and v= (frictional force/70) (is that right) but how do we get units in? and then frictinal force is the x component of the forces... but is there an f app?

 

[HallsofIvy]

You said you know how to integrate so I assume you have taken Calculus. What would the force and acceleration not being constant bother you?

Use ma= f. What does that look like in this case? What is f? Do you understand that a= dv/dt?

 

[ssm11s]

why didnt i think of that earlier. so dv/dt= -70v

divide both sides by v. then integrate one side in terms of dv and the other side in terms of t .
Thanks for the guidance !