Velocity-Friction proportionality.

[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.Using Newton's second law: F=ma 3. I'm guessing the acceleration is not constant in this problem. So the constant acceleration equations don't apply. I don't know how to include the time in this problem if i have no equations to solve them in.
Thanx in advance.

 

[rl.bhat]

At any instant Fr = 70* v.
Or retarding force ar = 70/1000*v Or
-dv/dt = 0.07*v or
-(dv/v) = 0.07*dt.
Take the integration between v to v/2 and find t.

 

[ssm11s]

Thank you so much ! makes perfect sense now !