Answer :

The acceleration of the object in the fluid is a = g – bv.

We know that acceleration is the derivative of velocity with respect to time.

Integrating with proper limits

As t approaches infinity, the exponential factor reaches zero. Thus, the object has a constant speed of g/b.

Alternative Way:

After a long time of release, speed is constant (say v^{’}) which implies there is no acceleration. Acceleration is given by

This implies, the constant speed v’= g/b.

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