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Why is average velocity=(v+u)/2

  1. Jun 13, 2009 #1
    Hi,

    I am reading through a study guide and currently going through the kinematics section.

    In the section on uniform acceleration it gives all the standard formulae and explains how they are derived.

    It says that average velocity = s/t, but also that it is equal to (v+u)/2 if the average velocity is uniform.
    Can someone explain this second part to me please? I understand the concept of averages and that we are dividing by 2 because we are only using 2 values, v and u. But through explaining the concept how does adding together v and u bring us the average velocity???

    Thanks.
     
  2. jcsd
  3. Jun 13, 2009 #2

    Doc Al

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    Staff: Mentor

    How about this:
    v = u + at (or: at = v - u)

    s = ut + 1/2at^2
    ave velocity = s/t = (ut + 1/2at^2)/t = u + 1/2at = u + 1/2(v - u) = (v+u)/2.
     
  4. Jun 13, 2009 #3
    Yes that makes sense, thanks.

    However in the book, it seems like it is saying that through a common sense approach this can be explained; i.e. not through using the other formulae.

    Here is how it is written in the book:

    DSC00205.jpg
    DSC00206.jpg
    DSC00207.jpg
     
  5. Jun 13, 2009 #4
    Does the forum software have a trim option to prevent this?
     
  6. Jun 13, 2009 #5
    It is the 3rd picture which contains the sentence that is causing me grief.
    It says 'Since the velocity is changing uniformly we know that this average velocity must be given by:

    average velocity = (v+u)2.

    Without using the other equations of uniform motion, why is this the case, why must it be given by (v+u)/2?
     
  7. Jun 13, 2009 #6
    To prevent what?
     
  8. Jun 13, 2009 #7

    Doc Al

    User Avatar

    Staff: Mentor

    There's nothing wrong with that. If something varies uniformly (linearly) that reasoning is fine. For example, if a flat incline goes from a height of 5 m to 25 m, what's the average height? Right in the middle, which is (5 + 25)/2 = 15 m.
     
  9. Jun 13, 2009 #8

    Doc Al

    User Avatar

    Staff: Mentor

    To prevent oversized attachments from messing up the formatting. (Which makes the posts harder to read.)

    I've seen this happen quite a bit. (I'll report it to the admins to see if there's a solution.)
     
    Last edited: Jun 13, 2009
  10. Jun 13, 2009 #9
    Oh right, sorry I should have reduced the size. Maybe I can edit it still?
     
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