(Solved): A 10-kg box moves along the \( x \) axis under the influence of a variable fo ...

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A 10-kg box moves along the \( x \) axis under the influence of a variable force. The potential energy is given by \( U(x)=10 x^{2}+7 x^{4} ; \) where \( x \) is in coordinate of the particle. The unit of potential energy is Joule \( (\mathrm{J}) \) and the unit of \( x \) is meter \( (\mathrm{m}) \). If the box has a speed of \( 23 \mathrm{~m} / \mathrm{s} \) when it is at \( x_{1}=2.0 \mathrm{~m} \), what is its speed when it is at \( x_{2}=3.0 \mathrm{~m} \) ? Please round your answer to one decimal place. Equation: Use the law of conservation of mechanical energy: \[ \begin{array}{lll} & U_{1}+\frac{1}{2} m v_{1}^{2}=U_{2}+\frac{1}{2} m v_{2}^{2} \quad U_{1}=U\left(x_{1}\right) \\ \text { and } & U_{2}=U\left(x_{2}\right) \end{array} \]