Calculating velocity of an object after very long time

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The problem involves calculating the velocity of a particle with acceleration defined as a = g - Kv, where g and K are constants. Starting from rest, the question seeks the velocity after a long time. The discussion raises concerns about whether the velocity will increase indefinitely or stabilize at a constant value. It is suggested that if the velocity approaches a constant, the acceleration would approach zero. The potential answers for the final velocity include g/K, 2g/K, and g/2K.
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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]
 
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