Problem

Iwo cars drive on a straight highway. At time $t=…

05:07

Problem 51 Medium Difficulty

$. .810$ Bacterial Motion Approximately 0.1$\%$ of the bacteria in an
adult human's intestines are Escherichia coli. These bacteria have
been observed to move with speeds up to 15$\mu \mathrm{m} / \mathrm{s}$ and maximum
accelerations of 166$\mu \mathrm{m} / \mathrm{s}^{2}$ . Suppose an $E$ . coli bacterium in your
intestines starts at rest and accelerates at 156$\mu \mathrm{m} / \mathrm{s}^{2}$ . How much
(a) time and (b) distance are required for the bacterium to reach a
speed of 12$\mu \mathrm{m} / \mathrm{s}$ ?

Answer

(a) 0.077 $\mathrm{sec}$
(b) 0.46$\mu \mathrm{m}$

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Physics 101 Mechanics

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Video Transcript

Okay, so and this problem, we have a bacteria and she starts from rest, which means well, initial velocity. Zero meters per second. The bacteria generates acceleration off 100 and 56 me crew meters per second square. And we want to discover time. Onda distance. The bacteria travels when she goes from zero two to ALF to a final velocity off 12 meet crew meters per seconds. Okay, so that's yes, it is right. We have a fine of a lawsuit. Traf meeker meters per second. So we have ah difference in velocity and we have acceleration so we can use velocity as a function of time and discover the time. So this time we have the final velocity 12 The initial velocity zero plus 156 D'oh! So that time is going to be 12 divided by 156 This is equal 0.77 0.770 point zero 77 Meet gross seconds. Me crew seconds. Okay. And what was the distance that the bacteria travel? It's calculating. Here. Going to have final velocity equals initial velocity to a delta X The final velocity throughout this square e cross to a a is 156 So that puts in this two times 156 don't X So did the East Inspector travel? I was just one for four, divided by 312. So the bacteria travels and the total distance off. Let's see 0.46 little 0.40 six make love meters 0.46 meat group meters. Actually, that time doesn't have to meet grow because you know, you know measuring me, Chris. Seconds, We're measuring seconds. Okay, So the total distance traveled by but by the bacteria was zero point 46 McCrum eaters in the total time was 0.77 That's the final answer. Thanks for watching.

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