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Distance/displacement integration problem

  1. Sep 27, 2012 #1
    1. The problem statement, all variables and given/known data


    Suppose that v(t)=t2 -2t -8, 1≤t≤6 is the velocity function (in meters per second) of a particle moving along a line. Find a) the displacement and b) the distance traveled by the particle during the given time interval.

    2. Relevant equations



    3. The attempt at a solution

    so i integrated the velocity function at the interval 1 to 6 and got the answer (-10/3)m. so i have no idea if this is the distance or displacement and if it is one of those, then how would i find the other one?

    thanks!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 28, 2012 #2

    Ray Vickson

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    Think about whether the particle can change its direction of travel between times 0 and 6, and if it can, think about what the integral ∫v(t): t=0..6 actually computes.

    RGV
     
  4. Sep 28, 2012 #3
    in the question it says that t can only be between 1 and 6 so i can't use any 0. and it is possible that the particle can change direction and my guess is this means that the integral ∫v(t): t=1 to 6 computes the distance. am i right?

    then how would i get displacement? can u give me a hint? i know that its the final position minus initial position but i don't know if i'm supposed to get it by integrating the function or do something else.
     
  5. Sep 28, 2012 #4

    ehild

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  6. Sep 28, 2012 #5

    HallsofIvy

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    v(t)=t^2 -2t -8, 1≤t≤6
    When t= 6, v(6)= 36- 12- 8= 16.
    When t= 1, v(1)= 1- 2- 8= -11.
    Now, what was the displacement? (Do you know what "displacement" means?)
     
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