Calculating velocity of an object after very long time

[Nikhil faraday]

Homework Statement

Acceleration 'a' of a particle moving in a straight line as a function of velocity 'v' is given as a = g-Kv where 'g' and 'K' are constans . if the object starts from rest then velocity of the object after very long time is ?[/B]

Homework Equations

a= v dv/dx
I don't know exactly what equation should be used

The Attempt at a Solution

Not getting any idea to solve it due to the problem statement which is given as to "calculate the velocity of the object after very long time".
The options given are:
1) g/k
2) 2g/k
3) g/2k
[/B]

 

[haruspex]

Will the velocity increase without limit? What would happen to the acceleration if it did?
If the velocity tends to some constant value, what does the acceleration do?