The terminal speed of a falling ball

A glass bead of radius $2.0\ \text{mm}$ is dropped from rest into glycerine. You will make the program step its speed forward a hundredth of a millisecond at a time, compare the speed it levels off at with the formula, and find how long it takes to reach $95\%$ of it.

The idea. Three forces act: the weight $mg$, the buoyancy $\tfrac43\pi r^3\sigma g$, and Stokes' drag $6\pi\eta rv$. The acceleration is their total over $m$. The terminal speed is $v_t = \dfrac{2r^2(\rho - \sigma)g}{9\eta}$.

Your tasks.

1. Inside the loop, work out the acceleration a from the three forces.
2. Work out the terminal speed vt from the formula.
3. Find the time at which the speed first reaches $95\%$ of vt.