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Homework Help: Vector jerk is the 3 derivative?

  1. Sep 18, 2010 #1
    1. The problem statement, all variables and given/known data
    r(t)=(5.00t2x + 12.5t3y meters
    The position r of a 12.0 kg mass, moving in the x-y plane




    2. Relevant equations
    Third derivative....
    sqrt(x2+y2)


    3. The attempt at a solution
    Is it correct to just take the third derivative and plug in 12 kg and find the magnitude and that would be a jerk?
     
  2. jcsd
  3. Sep 18, 2010 #2

    PhanthomJay

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    X*.*X: No.
    Now first off, those x and y variables are actually x_hat and y_hat unit vectors (usually denoted as i and j unit vectors). It means the position of the mass is at any time t is 5t^2 meters in the x direction and 12.5t^3 meters in the y direction. Were you not paying attention last time in your very first post to this forum??:wink: The third derivative is the rate of change with acceleration with respect to time (affectionately called a jerk). What's mass got to do with it?
     
  4. Sep 18, 2010 #3
    i was!
    So i cant do this?!
    r(t)=(5.00t^2x + 12.5t^3y)dt

    r(t)=10t +37t^2 --> velocity m/s 1st derivative

    r(t)=10 +74t ---> Acceleration m/s^2 2nd derivative

    r(t)=74 ----> Jerk m/s^3

    okay ha now im lost so is the answer 74 m/s^3 orrr

    sqrt(74 + 0)
     
  5. Sep 18, 2010 #4

    PhanthomJay

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    note my correction, where the bold letters represent unit vectors
    yes, and note bold unit vectors
    yes
    , yes, in what direction??
    Scratch that last answer, please. Say, if the Sox beat the Yanks 6 straight, we got a chance! Are you any good at Probabilities?
     
  6. Sep 18, 2010 #5
    Hmm so the final answer "in unit vector form" is 74y_^ m/s^3

    I'd say im decent :P havnt taken stats though but i do believe in getting lucky!
     
  7. Sep 18, 2010 #6

    PhanthomJay

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    Yes correct! And now I see what you were trying to do with that square root thing, using Pythagorus as your guide...but its jerk = square root of (0^2 + 74^2), or jerk = 74m/s^3 in y direction, same result!
    Excellent, my friend!

    edit: oops, math error, 12.5 x 3 =37.5, so the answer for jerk magnitide is 75, not 74, no biggy.
     
    Last edited: Sep 18, 2010
  8. Sep 18, 2010 #7
    ah yeah i was rushing :p Thanks again! Still trying to figure out how to actually write down my answer

    Answer box is given J=_______________ m/s3

    J=_____75y__________ m/s3
     
  9. Sep 18, 2010 #8

    PhanthomJay

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    Since J is in the y direction, you'd have to give the answer in unit vector form, J =75y_hat....I don't know how the answer box handles vector notation....probably in the same way x and y was noted in the original equation for r.
     
  10. Sep 18, 2010 #9
    Yeah its 75y_hat, thats how things are displayed in my notes! awesome once again you save the day! Now on to 2 blocks 1 pulley on an incline problem! ha this should only take me a few hours!
     
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