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Ok first off the reason its bonus is cause it involves using integration (which we haven't covered yet)

But our teacher says thats what makes it a bonus problem.

Ok here is the problem.

A 1000 kg boat is traveling at 90 km/h where its engine is shut off. The magnitude of the frictional force f(k) between boat and water is proportional to the speed v of the boat: f(k) = 70v, 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.

1000 kg - boat

90 km/h - 25 m/s

45 km/h - 12.5 m/s

f(k) = 70v

a = dv/dt

f(k) = ma

f = (1000 kg)(dv/dt)

Integration Rule.

f(V) = V^X -> f(V)dt = (V^X+1/X+1) + C

dt = 1000kg (70v^2/2) + C

dt = 1000 kg 35v^2 + C

dt = ?

(yea....i'm not sure where to from here...)

Um, yea. Any help would be appreciated.

Thanks,

Tony Zalles