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Calc 1 Riemann Sums w/ velocity and distance

  1. Nov 29, 2009 #1
    1. The problem statement, all variables and given/known data

    This is somewhat a repost... except I have figured out some of it and I have cleaned up the question.

    Your task is to estimate how far an object traveled during the time interval 0<= t >= 8 , but you only have the following data about the velocity of the object.

    [tex]\frac{time (sec)}{velocity (feet/sec)}\frac{0}{4}\frac{1}{1}\frac{2}{-2}\frac{3}{-3}\frac{4}{-4}\frac{5}{-3}\frac{6}{-1}\frac{7}{-3}\frac{8}{-1}[/tex]

    "See the attached graph."

    (PART 'A') Using the left endpoint Riemann sum, find approximately how far the object traveled. Your answers must include the correct units.

    Total displacement = "I have 11ft which is the right answer."

    Total distance traveled = "I cannot figure this out"




    2. Relevant equations

    Distance = time * velocity
    Displacement = time * velocity


    3. The attempt at a solution
    So I went ahead and got the Riemann sum of the left endpoint on the graph below.

    [tex]\Delta[/tex]X = 1

    So I just added the y values.

    The sum added up to -11 which was the answer for the displacement. I do not know why this is not the answer for the total distance but maybe I am missing something elementary.
     

    Attached Files:

    Last edited: Nov 29, 2009
  2. jcsd
  3. Nov 29, 2009 #2
    To find the distance traveled find the area of the shaded region. Area is always positive BTW :D
     
  4. Nov 29, 2009 #3
    I tried to compute the area, but I am not getting it. Also area if area is always positive then why would the area of a curve under the x axis be negative?
     
  5. Nov 29, 2009 #4
    Distance can never be negative.
     
  6. Nov 29, 2009 #5
    O.k. that actually makes tons of sense (I figured I was making some elementary mistake). So, I added up the areas as positive numbers and everything was correct. Thanks for the help.
     
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