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1D Kinematics Question

  1. Aug 5, 2007 #1
    I have just started out with Physics, so please don't expect to much :)

    I've tried by myself to figure out where x = vt + ½t² comes from; I know (because i've read) how to deduce it from a v versus t graph, and that it only works with a constant acceleration.

    My question is as follows:

    If -for any instant in time- :
    v = x / t
    a = v / t
    are true; Then, if i do this:

    x = vt and v = at
    Then subsitute the second in the first:
    x = at²
    I obviously miss the ½-factor from the area under the graph..
    What does this formula (x=at²) tell me in this case? I don't really see why exactly this wouldn't also give me the displacement..

    Could anyone be so kind to clear this up for me :) I'd hate to constantly have this question in the back of my mind.. just knowing that 'this is how it is'..

    Thanks in advance!
    Evert
     
  2. jcsd
  3. Aug 5, 2007 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Since the speed is not constant, [itex]\Delta x / \Delta t[/itex] gives the average speed, not the final speed at time t.

    For constant acceleration, the average speed is given by:
    [tex]v_{ave} = (v_i + v_f)/2[/tex]

    So, if you start from rest (t=0, v_i=0, x=0), then [itex]v_f = 2 v_{ave} = 2x/t[/itex].

    That should explain your missing ½-factor.
     
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