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Postion -> Velocity -> Acceleration -> Jerk ->?

  1. Feb 8, 2008 #1
    We all know that, assuming [tex]x(t) =[/tex] position as a function of time, then:

    [tex]x'(t) = v(t) = velocity[/tex]
    [tex]x''(t) = v'(t) = a(t) = acceleration[/tex]
    [tex]x'''(t) = v''(t) = a'(t) = j(t) = jerk[/tex] (assuming j is the symbol for jerk).

    But what does [tex]x''''(t) = j'(t)[/tex] come out to be? Is there a fourth derivative of position? And if so, is it ever practically used?

    What about fifth, sixth, seventh, etc derivatives?

    This is just something I've been extremely curious about since I learned of the third derivative, jerk (or jolt).

  2. jcsd
  3. Feb 8, 2008 #2

    'snap', 'crackle' and 'pop'.....:rofl:
  4. Feb 8, 2008 #3
    Haha that's funny.

    Does anyone happen to have a position/time graph in which you'd be able to calculate something like the fifth or sixth derivative of x? Would these ever even be needed? Hah.
  5. Feb 8, 2008 #4
    Anything that is a harmonic function, like say a pendulum, will have a non zero nth order x^n derivative thing.

    say, x = Sin(t)
  6. Feb 9, 2008 #5


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    Derivatives of order 4 & 5 can be used to find and classify the maximum/minimum accelerations, for example.
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