A particle experiences a force given by F(x) = α

Question

A particle experiences a force given by F(x) = α - βx³. Find the potential field U(x) the particle is in. (Assume that the zero of potential energy is located at x = 0.) A) U(x) = -αx + x⁴ B) U(x) = αx - x⁴ C) U(x) = 3βx² D) U(x) = -3βx²

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The Answer of A particle experiences a force given by F(x) = α - βx³. Find the potential field U(x) the particle is in. (Assume that the zero of potential energy is located at x = 0.) A) U(x) = -αx + x⁴ B) U(x) = αx - x⁴ C) U(x) = 3βx² D) U(x) = -3βx²