Results 1 to 4 of 4

Math Help - Differential equation

  1. #1
    Junior Member
    Joined
    Mar 2009
    Posts
    32

    Differential equation

    Hi,
    I am kinda having trouble with the following problem:

    Suppose that the acceleration of a model rocket is proportional to the difference between 120 ft/sec and the rocket's velocity. If it is initially at rest and its initial acceleration is 120 ft/sec^2, how long will it take to accelerate to 96 ft/s?
    t = ______________ sec


    What I have tried:

    dv/dt=k(120-v)

    integrating both sides:

    -ln|120-v| = t + C

    Since, t = 0 and initial velocity v = 0

    Thus, C = -ln|120|

    I am stuck here:

    Please help,

    Many thanks....
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,628
    Thanks
    430
    Quote Originally Posted by althaemenes View Post
    Hi,
    I am kinda having trouble with the following problem:

    Suppose that the acceleration of a model rocket is proportional to the difference between 120 ft/sec and the rocket's velocity. If it is initially at rest and its initial acceleration is 120 ft/sec^2, how long will it take to accelerate to 96 ft/s?
    t = ______________ sec

    a = k(120-v)

    a(0) = 120 , v(0) = 0

    120 = k(120) ... k = 1


    \frac{dv}{dt} = 120-v

    \frac{-dv}{120-v} = -dt

    \ln|120-v| = -t + C

    120-v = Ae^{-t}

    v = 120 + Ae^{-t}

    v(0) = 0

    0 = 120 + A ... A = -120

    v = 120(1 - e^{-t})<br />

    a = 120e^{-t}

    96 = 120e^{-t}

    solve for t
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2009
    Posts
    32

    Ans not right!!!

    Hi, for t I got 0.22314 or ln(120/96) but its not right....


    Please help,

    I have 1 trial left.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,628
    Thanks
    430
    ... how long will it take to accelerate to 96 ft/s?
    I misread the statement ... 96 ft/s is a velocity

    96 = 120(1-e^{-t})

    now solve for t
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: May 8th 2011, 12:27 PM
  2. Replies: 1
    Last Post: April 11th 2011, 01:17 AM
  3. [SOLVED] Solve Differential equation for the original equation
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: February 21st 2011, 01:24 PM
  4. Partial differential equation-wave equation(2)
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: September 6th 2009, 08:54 AM
  5. Partial differential equation-wave equation - dimensional analysis
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: August 28th 2009, 11:39 AM

Search Tags


/mathhelpforum @mathhelpforum