A single conservative force \( F(x) \) acts on a \( 1.0-\mathrm{kg} \) particle that moves along...

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A single conservative force \( F(x) \) acts on a \( 1.0-\mathrm{kg} \) particle that moves along the \( x \)-axis. The potential energy \( U(x) \) is given by \( U(x)=20+(x-2)^{2} \) where \( x \) is in meters. At \( x=5.0 \mathrm{~m} \), the particle has a kinetic energy of \( 20 \mathrm{~J} \).
Determine the equation of \( F(x) \) as a function of \( x \).
(1) \( F=2+x \)
(2) \( F=2+3 x \)
(3) \( F=2(2-x) \)
(4) \( F=3+2 x \)
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