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Homework Help: Average and Final Velocity

  1. Mar 9, 2004 #1
    I got this problem and it just stumped me. Can anyone give me the solution? Anyways, here's the question:
    Show that the average velocity of a body undergoing constant acceleration, and starting from rest. is half of its final velocity.

    Thanks in advance
     
  2. jcsd
  3. Mar 9, 2004 #2
    i was trying to solve your problem with some made up #'s but i couldn't get the V average to equal Vf. It may be my methods.....
     
  4. Mar 9, 2004 #3
    Sounds like you're already given the solution. The trick is getting there, right?

    Why don't you show us what you've tried so far?

    cookiemonster
     
  5. Mar 9, 2004 #4
    well if you take the initial V plus the final V and average it out your going to get the average V. (0+Vf)/2=1/2Vf I hope that helps
     
  6. Mar 9, 2004 #5

    NateTG

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    Homework Helper

    There's a nifty equation for constant acceleration which essentially gives you the answer.

    [tex]\vec{x}=\vec{x}_0+\frac{\vec{v}_0+\vec{v}}{2}t[/tex]

    You can also derive it from:
    [tex]\vec{x}=\vec{x}_0+\vec{v}_0t+\frac{1}{2}\vec{a}t^2[/tex]
    and
    [tex]\vec{v}=\vec{v}_0+\vec{a}t[/tex]
    by solving the bottom equation for [tex]t[/tex] and substituting in to the top one.
     
  7. Mar 10, 2004 #6

    HallsofIvy

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    Assuming constant acceleration, a, then the speed after time t is
    vf= v0+ at (so that t= (vf-v0)/a ) and the distance moved is v0t+ (1/2)at2.

    At constant speed, u, the distance moved would be
    ut. The average speed must move you the same distance as the actual speed in time t: ut= v0tf+ (1/2)at. Solve for u, then replace t by vf-v0)/a.
     
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