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Find the antiderivative of the following vector:

  1. Oct 14, 2015 #1
    1. The problem statement, all variables and given/known data
    Calculate the position vector of a particle moving with velocity given by:

    v = (32 m/s - (5 m/s^2 )t i) + (0 j)

    2. Relevant equations

    (x^(n+1) / (n+1) ) + C = antiderivative of function

    3. The attempt at a solution

    r = (32t m - (5/2)t^2 m/s + C m i) + (C j)

    Honestly, I'm just confused with the units more than anything. I don't know why the problem has m/s^2 if it's a velocity vector...
     
  2. jcsd
  3. Oct 14, 2015 #2

    SteamKing

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    A quantity of 5 m/s2 indicates that accelerated motion is taking place, i.e., the velocity is changing w.r.t. time. Acceleration × time = change in velocity.
     
  4. Oct 14, 2015 #3
    oooooh okay that makes more sense. thank you!

    and the antiderivative is right, right?
     
  5. Oct 14, 2015 #4

    SteamKing

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    I would say that since the velocity vector had no j-component, the position vector will not either.
     
  6. Oct 14, 2015 #5
    but isn't the antiderivative of 0 C (or in this case, D to differentiate)?
     
  7. Oct 14, 2015 #6

    SteamKing

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    Yeah, but D = 0 would be an acceptable value for the constant of integration, in the absence of any other initial condition information.
     
  8. Oct 14, 2015 #7
    oh okay. since this is on a take home test, do you think I should just put both answers (one for a definite integral 0 and one for an indefinite integral D)?
     
  9. Oct 15, 2015 #8

    SteamKing

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    You can have a definite integral only if you know the value of t.
     
  10. Oct 15, 2015 #9
    hmm... so what should I put down?
     
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