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Definite Integral

  1. Jul 8, 2004 #1
    Please help me! I got stuck on this problem:
    (1) A ball is dropped from rest, and after t seconds its velocity is v ft/sec. Neglecting air resistance, show that the average velocity during the first T/2 seconds is 1/3 of the average velocity during the next T/2 seconds.
    Will I integrate v? If so, what it is a function of?
     
  2. jcsd
  3. Jul 8, 2004 #2
    [tex]v(t)=gt[/tex]
    [tex]<v_1>=\frac{1}{\frac{T}{2}}\int_0^{\frac{T}{2}}gtdt[/tex]
    [tex]<v_2>=\frac{1}{\frac{T}{2}}\int_{\frac{T}{2}}^Tgtdt[/tex]
    [tex]T=\frac{v}{g}[/tex]
    You can figure out the rest I think.
     
    Last edited: Jul 8, 2004
  4. Jul 8, 2004 #3
    v is a function of time. Do you remember how to obtain the average of a function over an interval?
     
  5. Jul 22, 2004 #4
    A = 1/(b-a) S f(x) dx, where S is the intergral from a to b as ur limits
     
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