Final answer:
Bacteria often exhibit small displacement relative to the large distances they travel due to their frequent changes in direction, a process governed by chemotaxis.
Step-by-step explanation:
Bacterial Movement and Displacement
Bacteria use their flagella to move back and forth with speeds that can reach up to 50 µm/s (50 x 10-6 m/s). Despite traveling large total distances, the displacement of a bacterium is often small. This is because bacteria frequently change direction due to their response to environmental signals like chemical gradients in a behavior called chemotaxis. In this process, bacteria alternate between running and tumbling; they have longer runs and shorter tumbles when moving toward an attractant, which results in a more directed movement. In the absence of such gradients, their movement is more random, with runs and tumbles being more equal in length, leading to a limited overall displacement despite the significant distance covered.
When considering why the total distance traveled is large but displacement is small for bacteria, the most accurate reason is that bacteria change direction frequently. This is especially evident in the absence of chemical attractants or repellents, where movement is largely random, causing the path taken by the bacteria to be convoluted and often looping back on itself.