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How do you derive this? SImple question

  1. Mar 12, 2012 #1
    Derive for time!
    D=Vit+1/2at^2

    THANKS for you help
     
  2. jcsd
  3. Mar 12, 2012 #2
    The displacement is given by the area under the velocity-time graph. Your velocity-time equation is:
    [tex]
    v(t) = v_i + a t
    [/tex]
    and between the vertical lines [itex]t_1 = 0[/itex] and [itex]t_2 = t[/itex]. The geometric figure is a right trapezoid (trapzium outside U.S.) and the area is:
    [tex]
    D = \frac{1}{2} \left[ v_i + (v_i + a \, t) \right] \cdot t = v_i \, t + \frac{a \, t^2}{2}
    [/tex]
     
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