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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?

  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


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    Science Advisor
    Homework Helper

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


    You can also derive it from:
    by solving the bottom equation for [tex]t[/tex] and substituting in to the top one.
  7. Mar 10, 2004 #6


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    Science Advisor

    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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