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Find the constant c given quadratic equation F=

  1. Feb 23, 2013 #1
    A force F=(cx-3.00x2)i acts on a particle as the particle moves along an x axis, with F in newtons, x in meters, and c a constant. At x = 0 m, the particle's kinetic energy is 18 J; at x = 5 m, it is 12 J. Find c.


    I guess I don't understand the relationship between force and kinetic energy...
  2. jcsd
  3. Feb 23, 2013 #2


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    Hint: The work done by the force is equal to the change in kinetic energy.

    How is Work Done by a force defined in terms of an integral?
  4. Feb 23, 2013 #3

    rude man

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    F = ma = dv/dt
    Use chain rule to get from dv/dt to dv/dx
    Come up with the differential equation relating F(x) to v and dv/dx
    Solve. This results in a constant of integration plus you will still have c in the equation.
    So, need 2 equations since you have 2 unknowns. Use the given boundary conditions to solve for both constants.
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