Question

When engine was turned off,boat with mass m was moving with speed v_0.
The force of friction F=-αν-βv^2.
How long it would take to drop speed of boat 3 times?
Find the distance which the boat will travel in this time.

think i should try to solve differental equation in form of
md(v_0)/dt=-αν-βv^2

But I realy dont know what to do next,could someone,please help me with some steps or tips?

Answer 1

f=m (dv/dt)=-αν-βv^2
solve it then put vel=v/3
integrate |v|dt which will give distance travelled

Answer 2

\[\int\limits_{0}^{v/3} dv/-αν-βv^2=\int\limits_{0}^{t} dt\]

Answer 3

I do not uderstand why I should integrate from 0 to v/3 not from v_0 to v_0/3?