**Question:**

**An object falling through a fluid is observed to have acceleration given by a = g – bv where g = gravitational acceleration and b is constant. After a long time of release, it is observed to fall with constant speed. What must be the value of constant speed?**

**Solution:**

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