Calculating Time for a Boat to Slow Down Using Friction and Kinematics

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To calculate the time for a 1000 kg boat traveling at 90 km/h to slow down to 45 km/h after the engine is shut off, the frictional force is given by fk = 70v, where v is the speed in meters per second. The acceleration can be expressed as a = -0.07v, leading to the differential equation m(dv/dt) = -70v. By solving this equation, the time required for the boat to decelerate to the desired speed can be determined. The discussion highlights the initial confusion regarding the calculations, but ultimately, the solution was found. Understanding the relationship between speed, friction, and acceleration is crucial for solving such problems.
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A 1000 kg boat is traveling at 90 km/h when its engine is shut off. The magnitude of the frictional force, fk, between boat and water is proportional to the speed, v, of the boat: fk = 70v, where v is in meters per second and fk is in Newtons. Find the time required for the boat to slow to 45 hm/h.

Now, I have absolutely no clue as to what to do. I've tried a lot of different things and they have all led absolutely nowhere. I do know however that the a = 0.07v. Thats about all i can say for sure :cry: . Could someone nudge me in the right direction?
 
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Does this help?

m\frac{dv}{dt} = -70v
 
Never mind, i figured it out.
 
Yes it did tide, but you were about 10 seconds to late :P.
 

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