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Average rate

  1. May 3, 2008 #1
    the rate at which water is sprayed is given by the function f(t)

    during the time interval 0<t<4, what is the average rate of water flow??

    I'm confused whether to use the formula

    f(4)-f(0) / (4-0)


    [tex]\frac{1}{4}[/tex][tex]\int[/tex]f(t) evaluated from 0 to 4.

  2. jcsd
  3. May 3, 2008 #2


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    Hi fiziksfun ! :smile:

    Hint: Suppose f(t) is a constant, C. Then f(4) = f(0) = C.

    So which formula is right? :smile:
  4. May 4, 2008 #3
    i'm kind of slow, so i still don't understand :[
    can you help me more??
  5. May 4, 2008 #4


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    Sure! :smile:

    If f(t) = C, a constant, then obviously the average of f(t) is C.

    But f(4)-f(0) / (4-0) = (C - C)/4 = 0, which obviously is wrong. :frown:

    And ∫f(t)/4 = ∫C/4 (evaluated from t = 0 to 4) = C, which equally obviously is right! :smile:

    This works for any f(t), because f(t) is the rate of water, so ∫f(t) is the total water.

    And so the average rate of water = total/time = ∫f(t)/4. :smile:
  6. May 4, 2008 #5
    ah, i think i understand, thank you!!!
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