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Derivative as a rate if change - is this correct?

  1. Oct 8, 2006 #1
    I did this problem but wasnt sure if I did it right. Can anyone check it and see if my approach is correct?

    here is the question:
    The position of a moving body is given by s = f(t) = t^2 + 24t -1 for 0 <= t <= 8 where s is measured in meters and t in sec. Find the body's displacement for the time interval t = 3 to the time when the velocity is 34 m/s.

    here is what i did:
    s' = velocity = 2t + 24
    34 = 2t + 24
    t = 5

    so the time interval is 3 <= t <= 5
    t + delta t = 5
    t = 3

    displacement = f(t + delta t) - f(t)
    = (5^2 + 24*5 - 1) - (3^2 + 24*3 - 1)
    = 144 - 80
    = 64 meters

    I am wondering if this is correct. I wonder why they put the interval 0 <= t <= 8 ... maybe to throw us off. i dont know...

    thanks in advance
     
  2. jcsd
  3. Oct 8, 2006 #2
    yeah thats correct.
     
  4. Oct 8, 2006 #3
    thanks a lot!!
     
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