A) What is the magnitude of the bacterium\'s average velocity for the entire tri

Question

A)

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

B)

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

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 21 m/s . The following figure shows the trajectory of an E. coli as it moves from point A to point E (Figure 1) Figure 1 y ( m) 40 20 0 x (um) 20 40 80 100 20 -40

Explanation / Answer

Current Position of bacteria at E = - 40i - 20 j

Magnitude => |E| = (40^2 + 20^2)^1/2 = 44.72

Total distance travelled = ((50^2+10^2)^1/2 + 10 + (40^2+ 10^2)^1/2+(50^2+50^2)^1/2) = 172.93

Speed = 21

TIme = 8.23 s

Hence

a) average Velocity = 44.72/8.23 = 5.43

b) Direction = arcstan(-20/-40) = 26.57°

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