So I posted this earlier and it got to a point where differentiation is neccessary. I am a little familiar with differentiation, but not to the point where I know how to apply the concepts I have recently learned in Calculus. i would greatly appreciate somebody walking me through the process...it should be fairly simple in this particular problem. Again, this problem is for my own personal practice, not for a class, and I am very interested in finding out how to apply these concepts.(adsbygoogle = window.adsbygoogle || []).push({});

Thanks~Casey

Original Post:

1. The problem statement, all variables and given/known data

A 1000kg Boat is traveling 90km/h when its engine is cut. The magnitude of the frictional force fk is proportional to the boat's speed v: fk=70v, where v is in m/s and fk is in newtons. Find the time required for the boat to slow to 45 km/h.

2. Relevant equations

Newton's Second

V^2=Vo^2+2a(X-Xo)

X-Xo=VoT+1/2at^2

V=Vo+aT

3. The attempt at a solution

Vo=25m/s

V=12.5m/s

fk=70v=1750N

I drew a FBD and it seems that since the engine was cut, there is only fk in the x direction. Thus, fk=ma--->1750=-1000a-->a=-1.75

Then I used V=Vo+at---> t=(V-Vo)/a

-->t=(12.5-25)/-1.75=7.1

But this is not correct....9.9seconds is the correct solution.

Any advice is appreciated.

~Casey

...It was pointed out that "a" is not constant. But I am not sure where to go from here as I have only dealt with problems dealing with constant acceleration.....what am I differentiating? I am not sure of the equation...or how to derive one. hollah.

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# Still Friction

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