# Potential energy of a spring

As shown above, a red ball with a mass of $$2$$ kg is fixed on the right end of a spring with its left end fixed on the wall. The above right shows the potential energy $$E$$ of the spring as a function of the extension, denoted $$x,$$ of the spring (the distance between Point $$O$$ and Point $$A$$ in the left bottom picture). Which of the following statements is correct?

a) The spring constant of the spring is $$20$$ N/m.

b) $$80$$ N of force is needed to extend the spring by $$10$$ cm.

c) If we extend the spring by $$20$$ cm and let it go, the speed of the red ball at Point $$O$$ is $$4$$ m/s.

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