The only force acting on a 2.3 kg body as it moves along the positive x axis has an x component Fx = - 6x N, where x is in meters. The velocity of the body at x = 3.0 m is 8.0 m/s.
At what positive value of x will the body have a velocity of 5.0 m/s?
I'm not sure how to approach this. So far I have written down KE=(1/2)mv^2,
but I haven't the slightest idea where to go from here...

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  1. What you have is a spring-mass system, with spring constant 6.0 N/m.

    Total energy, which is constant, is
    (1/2)kX^2 + (1/2)MV^2
    = 3*9 + 1.15*64 = 100.6 J
    (using data at the X = 3.0 m location)

    Solve for X when V = 5 m/s

    100.6 = 3*X*2 + 1.15*25
    X^2 = 23.95 m^2
    X = 4.9 m

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