A single conservative force \( F(x) \) acts on a particle that moves along the \( x \)-axis. The...

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A single conservative force \( F(x) \) acts on a particle that moves along the \( x \)-axis. The graph of the potential energy with \( x \) is given. At \( x=5 \mathrm{~m} \), the particle has a kinetic energy of \( 50 \mathrm{~J} \) and its potential energy is related to position \( x \) as \( U=15+(x-3)^{2} \) Joule, where \( x \) is in meter.
(a) The mechanical energy of system is \( 69 \mathrm{~J} \).
(b) The mechanical energy of system is \( 19 \mathrm{~J} \).
(c) At \( x=3 \), the kinetic energy of particle is minimum
(d) The maximum value of kinetic energy is \( 54 \mathrm{~J} \).
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