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Need x= ? for d(x)/d(t)=c/x

  1. Sep 17, 2015 #1
    I have the equation v=c/x
    d(x)/d(t)=c/x
    velocity= c(constant)/x (distance)

    I need equations to calculate position, velocity and acceleration for a given time,
    My attempt was:
    xdx=cdt
    x2ln(x)=ct
    elnxx2=ekt
    xx2=ekt
    but I need x(t)v(t),a(t)

    Any suggestions on how to calculate?
     
  2. jcsd
  3. Sep 17, 2015 #2
    You start of well with ##xdx = cdt##
    The next step is wrong. How do you justify ##\int xdx = x^2 \text{ln}(x)##?
    Because that's what happens there.

    If you know ##x(t)## how can you find ##v(t)## and ##a(t)##?

    You've already used how you get ##v(t)##
     
  4. Sep 17, 2015 #3
    Where did the ln(x) come from??
     
  5. Sep 17, 2015 #4
    I did int of XDx= x2*(Dx/x)=
    x2LN(x)

    That was the wrong move...

    Thanks
     
  6. Sep 17, 2015 #5

    Mark44

    Staff: Mentor

    Usually, posters don't include enough parentheses, but here you have more than you need, which might have led to some confusion.

    The above can be written as ##\frac{dx}{dt} = \frac c x##. Separating, we get x dx = c dt. Integrating, we get ##\frac 1 2 x^2 = ct + K##.
     
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