A small spherical ball of mass \(m\) and radius \(R\) is dropped from rest into a liquid of high viscosity \(\eta\), such as honey, tar, or molasses. The only appreciable forces on it are gravity \(m g\) and a linear drag force given by Stokes's law, \(F_{\text {Stokes }}=-6 \pi \eta R v\), where \(v\) is the ball's velocity, and the minus sign indicates that the drag force is opposite to the direction of \(v\).

(a) Find the velocity of the ball as a function of time. Then show that your answer makes sense for

(b) small times;

(c) large times.