For a small particle of styrofoam (density (=19.2 mathrm{~kg} / mathrm{m}^{3}) ) that is spherical with a

Question:

For a small particle of styrofoam (density $=19.2 \mathrm{~kg} / \mathrm{m}^{3}$ ) that is spherical with a diameter $d=1.0 \mathrm{~mm}$ falling in standard air at speed $V$, the drag is given by $F_{D}=3 \pi \mu V d$ where $\mu$ is the air viscosity. Find

(a) the maximum speed of the particle starting from rest and

(b) the time it takes to reach $95 \%$ of this speed. Plot the speed $(\mathrm{m} / \mathrm{s})$ as a function of time.