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A conservative force, vec(F)=(6.0x-12)ha...

A conservative force, `vec(F)=(6.0x-12)hat(i)N`, where `x` is in meters, acts on a particle moving along an `x` axis. The potential energy U associated with this force is assigned a value of 27 J at `x=0`. (a) Write an expression for U as a function of `x`, with U in joules and `x` in meters. (b) What is the maximum positive potential energy ? At what (c) negative value and (d) positive value of `x` is the potential energy equal to zero ?

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The correct Answer is:
(a) `U= 27+12x-3x^(2); (b) U=39 J ; (c) x = -1.6 m ; (d) x = 5.6 m`.
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