🤓 Based on our data, we think this question is relevant for Professor Velissaris' class at UCF.

**A. **Average velocity:

$\overline{){{\mathbf{v}}}_{\mathbf{a}\mathbf{v}\mathbf{g}}{\mathbf{=}}\frac{\mathbf{N}\mathbf{e}\mathbf{t}\mathbf{}\mathbf{d}\mathbf{i}\mathbf{s}\mathbf{p}\mathbf{l}\mathbf{a}\mathbf{c}\mathbf{e}\mathbf{m}\mathbf{e}\mathbf{n}\mathbf{t}}{\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{}\mathbf{t}\mathbf{i}\mathbf{m}\mathbf{e}}}$

Net displacement is from O to E

$\begin{array}{rcl}\mathbf{N}\mathbf{e}\mathbf{t}\mathbf{}\mathbf{d}\mathbf{i}\mathbf{s}\mathbf{p}\mathbf{l}\mathbf{a}\mathbf{c}\mathbf{e}\mathbf{m}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{,}\mathbf{}{\mathbf{d}}_{\mathbf{O}\mathbf{E}}& \mathbf{=}& \sqrt{{\mathbf{x}}^{\mathbf{2}}\mathbf{+}{\mathbf{y}}^{\mathbf{2}}}\\ & \mathbf{=}& \sqrt{{\mathbf{40}}^{\mathbf{2}}\mathbf{+}{\mathbf{20}}^{\mathbf{2}}}\end{array}$

Net displacement = 44.7 μm

The bacterium *E. coli* is a single-cell organism that lives in the gut of healthy animals, including humans. When grown in a uniform medium in the laboratory, these bacteria swim along zigzag paths at a constant speed of 25 *μ*m/s. The following figure shows the trajectory of an *E. coli* as it moves from point *A* to point *E*.

(Figure 1)

Part A

What is the magnitude of the bacterium's average velocity for the entire trip?

Express your answer to two significant figures and include the appropriate units.

Part B

What is the direction of the bacterium's average velocity for the entire trip?

Express your answer using two significant figures.

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What scientific concept do you need to know in order to solve this problem?

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What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Velissaris' class at UCF.