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Rates of change calculus

  1. Apr 27, 2012 #1
    1. The problem statement, all variables and given/known data
    The kinetic energy K of a body of mass m is moving with speed v is given by..

    K = 1/2mv^2

    If a body's speed is increased by 2%, what is the approximate percentage change in it's kinetic energy...

    3. The attempt at a solution

    Δy ≈ f'(x) Δx

    ... f'(K) = mv Δx

    mv* 2?


    Don't know how to find the other values. Lol
  2. jcsd
  3. Apr 28, 2012 #2


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    Staff: Mentor

    Hi dimens. Let's write the equation: E= ½mv²

    and we are asked to consider the case where (∆v)/v = 0.02

    You have determined dE/dv = m⋅v

    and we will approximate the actual ∆E/∆v by using dE/dv.

    So far I have just restated what you provided. Can you complete this now?

    We use the equation: ∆E/∆v = ....... http://smilearchive.com/s/cwm/3dlil/idea.gif
  4. Apr 28, 2012 #3
    sorry i dont really get where you get the other variables from? E/0.02?
  5. Apr 28, 2012 #4


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    Staff: Mentor

    I just preferred E for K.E. because I thought E sounded more like an energy symbol! :smile:

    As for where did I get that 0.02 from? I got it here:
  6. Apr 28, 2012 #5
    but the answer is 4% i dont know where to get the other variables from :s
  7. Apr 28, 2012 #6


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    Staff: Mentor

    We don't need to get any more variables, we have all that is needed. The hard work has already been done. :smile: All that remains is some algebraic manipulation. So go back to my first post, follow through the steps as I've written them, and see whether you can complete the equation where I've indicated.
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