First complete:

• Propelling a Paramecium: 1 -- Equations 
• Propelling a Paramecium: 2 -- Estimations

1. Download the Excel spreadsheet,Paramecium.xlsx.  Copy out the formulas in row 7 (cells A7 through E7) and explain what each formula does in terms of the stepping rule for Newton's second law.
2. The values in the spreadsheet are arbitrary -- not related to the paramecium -- but never mind.  For now we will just explore how changing the parameters change the curves.  Notice that the velocity settles down to a constant and the net force and acceleration go to zero.  Explain why this happens.  (The velocity it settles down to is v_T and it's called the terminal velocity.)
3. Notice two things about the velocity plot:  what value it goes to (v_T) and how fast it settles down.  By changing the values for m, R, β, and F^appin the spreadsheet,  describe how these two things change as a function of each of these variables and why you think it does that.
4. Now try the numbers you generated for your paramecium in part 2 of the problem (including using a small fraction of the time scale you found as dt).  Find a value of F^app that gives a reasonable motion that settles down to a constant velocity in the time shown on the graph.  What is the value of F^app and dt that you found?  Print out and include your graphs for the paramecium.