Which of the following statements are true if a particle can move only along the

Question

Which of the following statements are true if a particle can move only along the x axis and is acted on by only one force. U(x) is the potential-energy function associated with this force. (Select all that apply.)

1.The particle will accelerate in the -x direction if it is at a location where dU/dx > 0 2.The particle will be in equilibrium if it is at a location where dU/dx = 0. 3.The particle will be in neutral equilibrium if it is at a location where both dU/dx = 0 and d2U/dx2 > 0. 4.The particle will both be in equilibrium and have constant speed if it is at a section of the x axis where dU/dx = 0 throughout the section. 5.The particle will be in stable equilibrium if it is at a location where both dU/dx = 0 and d2U/dx2 > 0.

Explanation / Answer

The particle will accelerate in the -x direction if it is at a location where dU/dx > 0

as dU/dx = F and if dU/dx > 0 that means F>0 and so acceleration > 0

The particle will be in equilibrium if it is at a location where dU/dx = 0

as dU/dx = F and if dU/dx = 0 that means F = 0 so the system will be in equilibrium

The particle will be in stable equilibrium if it is at a location where both dU/dx = 0 and d2U/dx2 > 0

The particle will both be in equilibrium and have constant speed if it is at a section of the x axis where dU/dx = 0 throughout the section.

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