Movement of bacterium in the microscope

AI Thread Summary
The discussion focuses on calculating the average velocity and average speed of a bacterium observed under a microscope. The average velocity is determined using the formula v = Δr/Δt, resulting in a vector of (0.387i - 0.596j + 0.5k) μm^-1. The average speed is calculated as |v| = Δs/Δt, yielding a value of 0.869 μm/s. It is noted that if the bacterium took a non-linear path, the average speed could be significantly higher than the calculated value. For curved paths, optimization techniques or segment length calculations would be necessary to determine the true distance traveled.
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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)
 
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