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Work Kinetic energy using variable force

  1. Dec 29, 2016 #1
    1. The problem statement, all variables and given/known data
    The position of an object of mass 2 kg is changing as a function of time by the formula x(t) = 4t^3-6t. (a) find the work done by the forces acting on the particle between t=1 and t=3s. (b) What is the object's velocity when the force on it is zero?

    2. Relevant equations
    is my work for part (a) correct?
    I do not know how to approach b.

    3. The attempt at a solution
    I took the derivative of the equation
    12(t)^2 - 6 at t=1s and t=3s
    to find vi and vf (I have vi = 6 m/s and vf = 102 m/s).
    Then I used W = change in KE
    1/2 x 2(102^2) - 1/2 x 2 (6^2) = 10,368 J.
    Is that correct?
    I'm not sure how to start part b
     
  2. jcsd
  3. Dec 29, 2016 #2

    PeroK

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    And the time derivative of velocity is?
     
  4. Dec 29, 2016 #3
    Are you asking for the acceleration?
     
  5. Dec 29, 2016 #4

    PeroK

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    Yes. Acceleration. Does that help for part b?

    Your answer to a) is correct.
     
  6. Dec 29, 2016 #5

    gneill

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    kjamha, your Relevant equations aren't equations. You should place equations that you think are relevant to the type of problem being solved in that portion of the template.
     
  7. Dec 29, 2016 #6
    taking the derivative, I would get acceleration = 24t
    if F = 0, then 0 = 24t and t would have to be 0
    find the velocity at time 0
    12(t)^2 - 6 = -6
    is the answer -6 m/s?
     
  8. Dec 29, 2016 #7
    ok - I read it quickly and thought it said relevant questions.
     
  9. Dec 29, 2016 #8

    PeroK

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    Yes, that's correct.
     
  10. Dec 29, 2016 #9
    Thank you!
     
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