Problem 3.40 The bacterium E. coli is a single-cell organism that lives in the g

Question

Problem 3.40 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 mu m/s . The following figure shows the trajectory of an E. coil 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. clockwise from positive direction of x-axis

Explanation / Answer

average velocity=total displacement/total time

to calculate total time taken, net distance covered has to be calculated first.

path AB:

distance=sqrt(50^2+10^2)=51 um

path BC:

distance=20-10=10 um

path CD:
distance=sqrt(40^2+10^2)= 41.2311 um

path DE:

distance=sqrt(50^2+50^2)=70.7107 um

net distance covered=51+10+41.2311+70.7107=172.9418 m

then total time taken=172.9418/25=6.9177 seconds

now, net displacement=distance OE=sqrt(20^2+40^2)=44.7214 um

then average velocity=net displacement/total time=6.4648 um/sec

part 2:

direction is along OE.

angle with +ve x axis=arctan(-20/40)=26.5651 degrees

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