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The force exerted by a weird, stretchy cord at given displacements is shown in the above table. Experimentally the force is found to vary proportionally to the square of the displacement, i.e. $F(x) = -h x^{2}$ where $h$ is some constant.

If the potential energy at $x = 0 m$ is $U_{0} = 0 J$ as shown above, determine the potential energy at $x = 1.5 m$.

A

$1.13 J$

B

$2.25 J$

C

$4.50 J$

D

$6.75 J$

E

$7.50 J$

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