Answer Happy

A spherically-shaped motile bacteria of mass m and radius r swims vertically upwards in a column of viscous fluid at constant speed up. Assume the cell has an average density that is the same as the water. a. [3 pts) Determine the associated equation of motion (i.e., an expression for the bacteria's acceleration)
b. [8 pts) At t = 0, the bacteria turns its “motor" off. Determine an expression for its position as a function of time z(t). Make sure to clearly indicate your chosen coordinate system. Assume the dynamics are linear.
c. [10 pts) Now assume the bacteria has a density twice that of the surrounding fluid. Determine its velocity as function of time after the motor is turned off. Also indicate what happens after a significant amount of time elapses (i.e., t+).
[4 pts) Stemming from the last part, determine the corresponding position as function of time.