Movement of bacterium in the microscope

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Homework Help Overview

The discussion revolves around the movement of a bacterium as observed through a microscope, focusing on calculating average velocity and average speed based on its position at two different times.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the calculation of average velocity and average speed, with one participant cautioning about the implications of the path taken by the bacterium. Questions are raised regarding the effects of a non-linear path on average speed and the need for optimization if the path is curved.

Discussion Status

Some participants express agreement with the initial calculations, while others introduce considerations about the path taken by the bacterium, suggesting that the average speed could be significantly higher if the path was not straight. There is an ongoing exploration of the implications of different movement paths.

Contextual Notes

Participants are considering the effects of the bacterium's movement path on the calculations, specifically addressing the assumptions made regarding straight versus curved paths. There is an acknowledgment of the need for additional information if the path is complex.

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Homework Statement



A biologist looking through a microscope sees a bacterium at r1→ = 2.2i + 3.7j -1.2kμm.
After 6.2s, it's at r2→ = 4.6i + 1.9kμm.
a)What is it's average velocity
b) What is its average speed

The Attempt at a Solution

a)
v→= Δr/Δt
v = (r2-r1)/6.2 = (2.4i - 3.7j + 3.1k)μm/6.2s
= (0.387i -0.596j + 0.5k) μm^-1

b)
|v| = Δs/Δt
|v| = SQRT[(2.4)^2i + (-3.7)^2j + (3.1)^2k]/6.2s
= 0.869μms^-1
 
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Looks good.
 
Caution: IF it went from the first location to the second location by a long and winding path,
then the average velocity will be the same but the average speed might have been many times that fast:
so that is a _minimum_ value for the average speed.
 
lightgrav said:
Caution: IF it went from the first location to the second location by a long and winding path,
then the average velocity will be the same but the average speed might have been many times that fast:
so that is a _minimum_ value for the average speed.

If the path was curved, I would have to utilize optimization, am I right?
 
if the path had been curved, you would need to find out long that path was
by adding each small segment length, found via pythagoras (or integrating the path if given a function with time)