A conservative force F ⃗ \vec{F} F =(4x-8)î N acts on a particle moving along the x-axis. The associated potential energy is 8 J at x=0. Which graph correctly represents U(x)?
Physics · Work , Power and Energy · conservative force and potential energy
JEE Mains NEET

Question

A conservative force F ⃗ \vec{F} F =(4x-8)î N acts on a particle moving along the x-axis. The associated potential energy is 8 J at x=0. Which graph correctly represents U(x)?

G1 Physics · Accepted Answer

F=-dU/dx=4x-8 gives dU/dx=8-4x. Integrating, U=8x-2x²+C; U(0)=8 gives C=8. Thus U(x)=-2x²+8x+8, the concave-down parabola shown in Image 1. Hence A.