4.3.2.P2

In his physics lab, Radagast has observed the motion of an E. coli bacterium using a video camera. His log-log plot of the square deviation of his chosen bacterium as a function of time is shown in the figure below. (The graph is presented in two equivalent forms: one for those who have used Excel – on the left – instead of log-log graph paper – on the right.) The bacterium seems to have two distinct behaviors: for times shorter than 1 second (marked A) and for times longer than 10 seconds (marked B).

Some possible ideas explaining the behavior of the bacteria in the two regions might include

1. The bacterium is moving purposefully in response to some chemical gradient.
2. The bacterium is moving at random in response to the thermal motion of its environment.
3. The bacterium is constrained in some way.
4. The bacterium is using its flagella (which work like propellers) to move at a constant velocity
5. The bacterium is accelerating in response to a force in a fixed direction.

Do you think any of these might explain the bacterium's behavior in region A? In region B? Say which you think might be the correct hypothesis for each of the two regions and explain what your evidence is in support of your choice. If you do NOT think any of these explanations could be possible, explain why you think so.

Joe Redish 2/1/13