The bacterium E. coli is a single-cell organism that lives in the gut of healthy

Question

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 24 ?m/s . The following figure shows the trajectory of an E. coli as it moves from point A to point E. (Figure shown below)

What is the direction of the bacterium's average velocity for the entire trip? (? clockwise from positive direction of x-axis)

Explanation / Answer

Given that

When grown in a uniform medium in the laboratory, these bacteria swim along zigzag paths at a constant speed of (v) =24 m/s

The Average velocity is given by

Net displacement /Total time

Here the net displacement is from final position E to O is Sqrt(402+202) =44.721um

Then length of AB is given by =Sqrt(102+502) =51um

And the time taken is given by =51/24 =2.125s

Then Length of CB is =10um

And the time taken is 10/24 =0.41667s

Length of CD =Sqrt(102+402) =41.23um

Time taken is =41.23/24=1.718s

Length of DE =Sqrt(502+502)=70.71um

The taken is =70.71/24 =2.946sec

Now therefore the average velocity is =44.721/(2.125+0.41667+1.718+2.946) =6.206um/s

Then it makes an anlge Arctan(20/40)=26.565 degree Clockwise with X-axis

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