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4 March, 07:43

A force F = (cx - 3.00x^2) i^ acts on a virus as the virus moves along an x axis, with F measured in Newtons, x in meters, and c a constant. At x = 0, the virus’s kinetic energy is 20.0 J, while at x = 3.00 m, it is 11.0 J. Find c.

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  1. 4 March, 08:22
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    c = 4

    Explanation:

    From work-energy theorem KE = workdone.

    Given F = (cx - 3.00x²) i

    W = ∫Fdx = ∫ (cx - 3.00x²) dx = cx²/2 - 3.00x³/3 + A

    W = cx²/2 - x³ + A

    Where A is a constant

    At x = 0, KE = 20J

    So W = 20J at x = 0

    20 = c*0 - 0 + A

    A = 20

    So W = cx²/2 - x³ + 20

    Also when x = 3.00m, W = KE = 11J

    So

    11 = c*3²/2 - 3³ + 20

    11 = 4.5c - 7

    4.5c = 11 + 7

    4.5c = 18

    c = 18/4.5 = 4

    c = 4
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