Question

Approximately 0.1% of the bacteria in an adult human's intestines are E. coli. These bacteria have been observed to move with speeds up to 15 μm/s and maximum accelerations of 166 μm/s2. Suppose as E. coli bacterium in your intestines starts at rest and accelerates at 156 μm/s2. How much time and distance are required for the bacterium to reach a speed of 12 μm/s?

Answer 1

Answer:

0.0769230769231 s

$4.6153846154\times 10^{-7}\ m$

Explanation:

t = Time taken

u = Initial velocity = 0

v = Final velocity = 12 μm/s

s = Displacement

a = Acceleration = 156 μm/s²

From the linear equations of motion we have

$v=u+at\\\Rightarrow t=\dfrac{v-u}{a}\\\Rightarrow t=\dfrac{12\times 10^{-6}-0}{156\times 10^{-6}}\\\Rightarrow t=0.0769230769231\ s$

Time taken to reach the required speed is 0.0769230769231 s

$s=ut+\dfrac{1}{2}at^2\\\Rightarrow s=0\times t+\dfrac{1}{2}\times 156\times 10^{-6}\times 0.0769230769231^2\\\Rightarrow s=4.6153846154\times 10^{-7}\ m$

The distance the bacterium will cover is $4.6153846154\times 10^{-7}\ m$