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?
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.
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