Solving Boat Motor Engine Equations w/ Integration

[betty0202]

Homework Statement

turning on the engine of a motorboat (v0=0),
K = constant force due to the engine
drag force of the water D = -cv
find v(t)=?

Homework Equations

integration
f=ma, a=dv/dt

The Attempt at a Solution

[/B]
D+K = MA
K-cv = MA
(A=dv/dt)
K-cv=Mdv/dt
Mdv=dt(K-cv)
?
i want to do integration on both side of the
equation but I can't isolate V

thanks

 

[gneill]

Mdv=dt(K-cv)

You need only gather the v and t terms on opposite sides of the equation. Constants can be on either side. Divide both sides by (K - cv).

 

[betty0202]

You need only gather the v and t terms on opposite sides of the equation. Constants can be on either side. Divide both sides by (K - cv).

I hope I did the math right $\int_{}^{} (\frac{m}{k-cv})dv=\int_{}^{}dt$
$-m\ln(cv-k)=t$
$\ln(cv-k)=-\frac{t}{m}$
$v=\frac{e^{-\frac{t}{m}}+k}{c}$
??

 

[gneill]

You'll want to write the integrals as definite integrals (with specified limits of integration), otherwise you need to introduce and deal with the constants of integration. The starting limits for each integral are simple: they're both zero.

 

[betty0202]

You'll want to write the integrals as definite integrals (with specified limits of integration), otherwise you need to introduce and deal with the constants of integration. The starting limits for each integral are simple: they're both zero.

thank you