Topic: Energy
Concepts: Potential energy graphs

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Solution:

Recall force is related to the potential energy by

so force is given by the negative slope of the $U$–$x$ plot. Part I and Part IV have zero slope so there is no force. Part II has slope $-1$ so the force is $+1\,\mathrm{N}$. Part II has slope $+1$ so the force is $-1\,\mathrm{N}$. Thus, the answer is E.

Topic: Energy
Concepts: Motion graphs, Potential energy graphs

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Solution:

• Graph I shows a particle staying at rest in a region where there is no force. This is allowed.
• Graph II shows a particle staying at rest in a region where is a force. This is not allowed.
• Graph III shows a particle moving at constant velocity in a region where there is no force. This is allowed.

Thus, the answer is D.

Topic: Energy
Concepts: Motion graphs, Potential energy graphs

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Solution:

The particle is trapped in the region where $U \leq -5\,\mathrm{J}$. Thus, the total energy is $E=-5\,\mathrm{J}$ since the particle has no kinetic energy at the endpoints where $E=U$. The answer is A.