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Find x dot as function of t

  1. Sep 28, 2008 #1
    1. The problem statement, all variables and given/known data

    find velocity x dot, as function of time t, for particle mass m starts x=0, t=0
    subject to force where Fo and c are constants.

    Fx = Fo + ct



    2. Relevant equations

    answer is

    x dot =Fo/m t + c/2m t^2

    3. The attempt at a solution


    obviously it is just an integration.
    but how does the "m" get in there.

    i know this is a simple question, but the solution eludes me

    i have stuff like

    Fo=c=constant
    F=ma
    F=mv dot = m r dotdot
    d=r=vt=dv/dt
    x dotdot = dv/dt = F/m = a = constant

    what is Fx - is the the force component in direction x , or is it a vector , ?
    what is Fo - a constant, vector?

    how do you add in a t


    how about

    Fx dt = Fo dt + ct dt

    Fo = ma = m v dot

    x dot = int Fo dt + int ct dt

    = int dt + 1/2 c t^2
    =

    ... and im lost
     
  2. jcsd
  3. Sep 28, 2008 #2

    gabbagabbahey

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    Gold Member

    [tex]F_x[/tex] is the x-component of the total force on the particle and so

    [tex]F_x=ma_x=m \ddot{x}=m \frac{d^2x}{dt^2}[/tex]

    Is that enough to get you started?
     
  4. Sep 28, 2008 #3
    i think i got it .....

    i did f=ma

    a = f/m = x dot dot


    so ....

    x dot = ∫ Fo/m +∫ ct/m

    is that the right method .....
     
  5. Sep 28, 2008 #4

    gabbagabbahey

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    Gold Member

    Looks fine so far (I'm assuming you're integrating over dt). What do you get?

    edit- make sure you include a constant of integration.
     
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