The concept used in this question will be based on the behaviour of a spherical object when it is dropped through a viscous fluid. When a spherical body of radius r is dropped, it is first accelerated and gradually the acceleration comes to zero, attaining a constant velocity which is known as terminal velocity.
Given,
a = g – bv
We know that,
a = dv/dt = 0 for uniform motion
g = gravitational acceleration
Therefore, it can be said that as the speed increases, acceleration decreases. When the speed is v0, acceleration will be zero and speed remains constant.
Therefore, a = g – bv0 = 0
v0 = g/b