First complete:

• Propelling a Paramecium: 1 -- Equations 

1. We are going to solve for the motion of the paramecium using a spreadsheet (like Excel or GoogleDocs) and a stepping rule.  To do that we need to choose a time step dt.  In any problem, we can get an idea of what the appropriate time scale is by creating a time out of the parameters.  By considering the dimensionality of the parameters β, m, and R [dimensionality means, M,L,T and their combination -- see the page Complex Dimensions and Dimensional Analysis] can you combine the three of these parameter as products or ratios so that the resulting combination has the dimensions of time?  This combination gives a natural time scale for the problem.
2.  Let's evaluate the natural time scale for the paramecium's motion. The value of β for water at room temperature is about 0.017 kg/m-s.  But we also need the mass of the paramecium.  Although a paramecium is stretched out a bit, let's take an oversimplified model treating it like a sphere.  An average radius  for a paramecium is about R = 1/4 mm.  Estimate the mass, m, of such a paramecium.  Discuss what density you choose and why. Combine these numbers to find the natural time scale for the motion of the paramecium.

Then complete:

• Propelling a Paramecium: 3 -- Calculations