The bacterium Escherichia coli (or E. coli ) is a single-celled organism that li

Question

The bacterium Escherichia coli (or E. coli) is a single-celled organism that lives in the gut of healthy humans and animals. When grown in a uniform medium rich in salts and amino acids, these bacteria swim along zig-zag paths at a constant speed of 20 m/s . The figure shows the trajectory of an E. coli as it moves from point A to point E. Each segment of the motion can be identified by two letters, such as segment BC.(Figure 1)

Part M

Calculate the total distance traveled.

Express your answer using two significant figures.

______

Part N

Calculate the magnitude of the net displacement for the entire motion.

Express your answer using two significant figures.

________

Part O

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

Express your answer using two significant figures.

_________

Part P

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

Express your answer using two significant figures.

_________

1 of 1The plot shows a trajectory on the xy plane. The values on the x axis are from zero to 100 micrometers. The values on the y axis are form 049 to 40 micrometers. Point A is at the origin. The next point is point B with x coordinate of 50 micrometers and y coordinate of 10 micrometers. The next point is point C with x coordinate of 50 micrometers and y coordinate of 20 micrometers. The next point is point D with x coordinate of 90 micrometers and y coordinate of 30 micrometers. The last point is point E with x coordinate of 40 micrometers and y coordinate of -20 micrometers.

The bacterium Escherichia coli (or E. coli) is a single-celled organism that lives in the gut of healthy humans and animals. When grown in a uniform medium rich in salts and amino acids, these bacteria swim along zig-zag paths at a constant speed of 20 m/s . The figure shows the trajectory of an E. coli as it moves from point A to point E. Each segment of the motion can be identified by two letters, such as segment BC.(Figure 1)

Part M

Calculate the total distance traveled.

Express your answer using two significant figures.

r =

______

  m  

Part N

Calculate the magnitude of the net displacement for the entire motion.

Express your answer using two significant figures.

|S | =

________

  m  

Part O

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

Express your answer using two significant figures.

|v | =

_________

  m/s  

Part P

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

Express your answer using two significant figures.

=

_________

   below + x-axes Figure

1 of 1The plot shows a trajectory on the xy plane. The values on the x axis are from zero to 100 micrometers. The values on the y axis are form 049 to 40 micrometers. Point A is at the origin. The next point is point B with x coordinate of 50 micrometers and y coordinate of 10 micrometers. The next point is point C with x coordinate of 50 micrometers and y coordinate of 20 micrometers. The next point is point D with x coordinate of 90 micrometers and y coordinate of 30 micrometers. The last point is point E with x coordinate of 40 micrometers and y coordinate of -20 micrometers.

40 30 10 10 20 30 40 5060 70 80 90 100 -10 -20 -30 40

Explanation / Answer

M) total distance travelled, r = AB + BC + CD + DE

= sqrt(10^2 + 50^2) + 10 + sqrt(40^2 + 10^2) + sqrt(50^2 + 50^2)

= 172.9 micro m

= 170 micro m (when rounding to two significant figures) <<<<<<------Answer

N) The magnitude of the net displacement, |s| = sqrt(40^2 + 20^2)

= 44.7 micro m

= 50 micro m (when rounding to two significant figures) <<<<<<------Answer

O) time taken, t = distance travelld/speed

= = 172.9/20

= 8.645 s

magnitude of average speed, |v| = |s|/t

= 44.7/8.645

= 5.17 micro m/s

5.2 micro m/s (when rounding to two significant figures) <<<<<<------Answer

P) theta = tan^-1(20/40)

= 26.56 degrees

= 26 degrees below +x axis (when rounding to two significant figures) <<<<<<------Answer

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