Results 1 to 3 of 3

Math Help - variable acceleration

  1. #1
    Newbie
    Joined
    Mar 2008
    Posts
    11

    variable acceleration

    Bit of help with this one if poss..

    A vehicle has acceleration

    f(t) = a/(1+t)^n

    where a > 0, n>1(n not equal 2) are const.

    Find x dot of (t) and x(t)

    x(0)=x dot x(0)=0

    what is the max speed poss??
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    so we have ...

    \frac{dv}{dt}=\frac{a}{(1+t)^n}

    This is a seperable ODE

    \int dv=\int \frac{a}{(1+t)^n}dt

    solving gives

    v=\frac{a(1+t)^{-n+1}}{-n+1}+C

    Using the intial condition v(0)=0

    we get

    0=\frac{a(1+0)^{-n+1}}{-n+1}+C

    so solving for C we get

    C=\frac{-a}{-n+1}=\frac{a}{1-n}

    So

    v=\frac{a(1+t)^{-n+1}}{-n+1}+\frac{a}{1-n}

    so now we get

    v=\frac{dx}{dt}=\frac{a(1+t)^{-n+1}}{-n+1}+\frac{a}{1-n}

    This is also a seperable ODE. So just repeate the process from above.

    You should be able to finish from here
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member chella182's Avatar
    Joined
    Jan 2008
    Posts
    267
    I don't understand how you know you get -a on the top when you're solving for C... in fact, n>1 so the power of the (1+0) is bound to be positive surely? Surely it should just be a?

    Also, I don't get where -n+1 has come from either
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Kinematics Aplication problem - variable acceleration.
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: November 7th 2010, 01:16 PM
  2. Replies: 2
    Last Post: May 3rd 2010, 12:38 AM
  3. Replies: 2
    Last Post: April 22nd 2010, 08:23 PM
  4. Variable acceleration
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 18th 2009, 10:21 AM
  5. variable acceleration
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 4th 2008, 06:57 AM

Search Tags


/mathhelpforum @mathhelpforum