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Moderate

Force-Position Integration with a Given Function

APPHMC-YOYLEF

A particle experiences a position-dependent force given by:

$$F(x) = -6x^{2}+4x+3/x^{2}$$

...where $x$ is in meters and $F$ is in Newtons (units have been abbreviated). Suppose the baseline potential energy is such that the constant of integration is zero ($C = 0 J$).

At $x = 1 \text { m}$, what is the potential energy of the particle?

A

$+5 \text{ J}$

B

$+3 \text{ J}$

C

$-3 \text{ J}$

D

$-5 \text{ J}$

E

Cannot be determined