Boat slowing down with variable acceleration

[ionitacodrut]

A motor boat of mass m moves on the surface of a lake at a speed0v. At the moment 0t= the engine is shut down. Assuming the resistance of water to be proportional to the speed of the boat, F=−rv, find
a) the time interval after which the boat stops;
b) the speed of the boat as a function of the distance covered with the shutdown engine.
I have tried using the kinetic variation law but can' exactly figure out the work done by F

 

[jbriggs444]

A motor boat of mass m moves on the surface of a lake at a speed0v.

There appears to be a typo in your post. The zero in "0v" is extraneous.

I would work on part a) first. Can you characterize the speed of the boat as a function of time?

If you know how to solve differential equations, there is a fairly simple one here. If not then you can notice that as the velocity of the boat is reduced the acceleration is reduced proportionally. So the fraction of the speed that bleeds off over a fixed time interval will be constant. That means that the speed must decay geometrically. So it can be modeled by a function like v = ce^-kt for some constants c and k. You solve the equation by finding values of c and k that fit the givens of the problem (and that is essentially how you solve the differential equation).