The force acting on a particle of mass m moving along the x-axis

• GP Work Energy

The force acting on a particle of mass m moving along the x-axis is given by F(x) = Ax² - Bx. Which one of the following is the potential energy of the particle?

1. 2Ax - B
2. -x²/6 (2Ax - 3B)
3. Ax³ - Bx²
4. Zero

Answer

Potential Energy = - ∫ F(x) dx

U(x) = - ∫ (Ax² - Bx) dx

U(x) = - Ax³/3 + Bx²/2

U(x) = -x²/6 (2Ax - 3B)

The correct option is B.