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Movement of bacterium in the microscope

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  1. Jan 17, 2014 #1
    1. The problem statement, all variables and given/known data

    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


    3. 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
     
  2. jcsd
  3. Jan 17, 2014 #2
    Looks good.
     
  4. Jan 17, 2014 #3

    lightgrav

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    Homework Helper

    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.
     
  5. Jan 17, 2014 #4
    If the path was curved, I would have to utilize optimization, am I right?
     
  6. Jan 19, 2014 #5

    lightgrav

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    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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