Randall D. Knight — Work and Kinetic Energy: Problem 66

A paramecium is an elongated unicellular organism approximately $50\ \mu\text{m}$ in diameter and $150\ \mu\text{m}$ in length. It swims through water by whip-like movements of cilia, small hairs on the outside of its body. Because it moves “head first” through the water, drag is determined primarily by its diameter and only secondarily by its length, so it’s reasonable to model the paramecium as a $70\text{-}\mu\text{m}\text{-diameter}$ sphere. A paramecium uses $1.5\text{ pW}$ of locomotive power to propel itself through $20^\circ\text{C}$ water, where $1\text{ pW} = 1\text{ picowatt} = 10^{-12}\text{ W}$. What is its swimming speed in $\mu\text{m/s}$?