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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 $x = 5 m,$ the particle has a kinetic energy of 50 J and its potential energy is related to position $' x'$ as $U = 15 + {(x - 3)}^{2}$ Joules, where $x$ is in meter. Then :

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The mechanical energy of system is 69 J

The mechanical energy of system is 19 J

At $x = 3,$ the kinetic energy of particle is minimum

The maximum value of kinetic energy is 54 J

answer is A, D.

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Detailed Solution

$U = 15 + {(x - 3)}^{2}$
$U_{\min} (x = 3) = 15 J$
$K E (x = 5) = 50 J$
At $x = 5, U (x = 5) = 15 + 4 = 19$
Total mechanical energy
$K E + U = 50 + 19$
$= 69 J$
Maximum $K E = 69 - 15$
$= 54 J$

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