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Velocity question

  1. Feb 7, 2006 #1
    Does anyone happen to know why the instantaneous velocity at the midpoint of a time interval is equal to the average velocity over the same time interval?? I can't seem to prove this reasoning.

    Thanks!! :smile:
  2. jcsd
  3. Feb 7, 2006 #2


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    Staff: Mentor

    You're talking about when acceleration is constant.... It's just from the definition of "average" - the 2 in the denominator is where you get the halfway point in time.
  4. Feb 8, 2006 #3


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    Homework Helper

    First note that the average velocity is midway between the two velocities values, [itex]v_1,\ v_2[/itex], at the endpoints of the interval. Since

    We therefore need to show that the time at which the average velocity is reached is in the middle of the time interval. In the drawing time is on the horizontal x-axis and speed on the vertical y-axis. What needs to be proved then in the drawing is that [itex]AD=BC[/itex], It is clear that both these length are given by
    [tex]\frac{\Delta v}{2\tan(\theta)}[/tex]

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    Last edited: Feb 8, 2006
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