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1D Kinematics

  1. Jan 24, 2015 #1
    Usually, equations of motion (with constant acceleration) are written in terms of values of position/velocity at time ##t=0##.
    Take for example:

    $$x = x_0 + v_0t + \frac{1}{2} a t^2$$

    Where ##x_0## and ##v_0## are the values (at ##t=0##) of position and velocity respectively.

    What if we're given position at some other time ##t=t_0##, instead of ##t=0##, and we're asked to find ##x## as a function of time?

    What I do is I find a more general form of the equation I wrote above as follows:

    $$\int_{x_0}^x dx' = \int_{t_0}^t v(t') dt'$$

    Where ##x_0## now represents position at time ##t=t_0##.

    Another way would be to eliminate the variable ##x(0)##

    Is there any alternative approach?
     
    Last edited: Jan 24, 2015
  2. jcsd
  3. Jan 24, 2015 #2
    This approach is great. Of course, what you would find is that you could also just substitute (t - t0) for t in the original equation (i.e., shift the time scale), assuming that v0 is the velocity at t = t0.

    Chet
     
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