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Homework Help: Higher Derivatives - Acceleration help

  1. Oct 20, 2009 #1
    1. The problem statement, all variables and given/known data
    A particle moves along the x-axis, its position at time t is given by
    [tex]$\displaystyle \Large x(t)=\frac{7 t}{6+5 t^2}, \ t\geq 0,$[/tex]
    where t is measured in seconds and x is in meters. The acceleration of the particle equals 0 at time t = ____ and ____ seconds.

    2. Relevant equations
    [tex]$\displaystyle \Large x(t)=\frac{7 t}{6+5 t^2}, \ t\geq 0,$[/tex]
    v(t) = x'(t)

    3. The attempt at a solution
    once i find a(t), which is the 2nd derivative of the original function, i get:
    [tex]$\displaystyle \Large a(t)=\frac{7t-7}{2t(6+5t^2)}[/tex]

    so when acceleration=0, [tex]$\displaystyle \Large a(t)=\frac{7t-7}{2t(6+5t^2)}=0[/tex]
    but what the other value?
  2. jcsd
  3. Oct 20, 2009 #2


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    You solved the derivatives incorrectly
  4. Oct 20, 2009 #3
    oh my bad. it should be:
    -440t / (6+5t^2)

    now what?
    Last edited: Oct 20, 2009
  5. Oct 21, 2009 #4
  6. Oct 21, 2009 #5
    You still do not have the correct second derivative. (I think).
  7. Oct 21, 2009 #6
    ok.. i give up. my algebra is good but i have no idea where to go.
    this is what i got for the second derivative after doing it 20 times to make sure i didnt make mistakes:
    [tex]$\displaystyle \Large x''(t)=\frac{ -70t(6+5t^2)-20t(42-35t^2) }{(6+5t^2)^2} \ $[/tex][tex]$\displaystyle \Large =\frac{ -1260t-1050t^3 }{(6+5t^2)^2} \ $[/tex]

    maybe im stuck on the factoring of (42-35t^2)... but i just dont know aaaah
  8. Oct 21, 2009 #7
    If that is the correct second derivative - and I have not checked - you are now looking for the points at which acceleration equals zero. So you set the second derivative equal to zero and solve for t.
  9. Oct 21, 2009 #8


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    2nd derivative is still wrong
  10. Oct 21, 2009 #9
    oh so the only thing i did wrong is including the 7 in my calculations all the time.. hh tnx man!

    David Gould - yeah i know that but the thing is i got 0 all the time and i needed another value so here i got it.. tnx
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