1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    russ_watters

    User Avatar

    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

    andrevdh

    User Avatar
    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
    [tex]v_1+\frac{1}{2}(v_2-v_1)=v_1+\frac{v_2}{2}-\frac{v_1}{2}[/tex]

    [tex]=\frac{v_1+v_2}{2}[/tex]
    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]
     

    Attached Files:

    Last edited: Feb 8, 2006
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Velocity question
  1. Velocity question (Replies: 5)

  2. Velocity question (Replies: 12)

  3. Velocity questions (Replies: 16)

Loading...