Topic: Energy
Concepts: Potential energy graphs

Solution:

Recall a particle moving in a potential energy landscape $U(x)$ experiences a force

• A) True because at $x=1\,\mathrm{cm}$ and $x=3\,\mathrm{cm}$, the slope of the $U$–$x$ plot is zero so there is no force at those points.
• B) True because the minimum possible kinetic energy is zero (particle at rest) and the minimum possible potential energy in this plot is $U=-10\,\mathrm{J}$ at $x=3\,\mathrm{cm}$.
• C) True because the slope at this point is about $10\,\mathrm{J/cm}=1000\,\mathrm{N}$.
• D) True because the minimum possible potential energy is $U=-10\,\mathrm{J}$ so if the total energy is $E=0\,\mathrm{J}$, then $K=E-U=10\,\mathrm{J}$.
• E) Not true because the slope at this point is about $-20\,\mathrm{J/cm}=-2000\,\mathrm{N}$. Since the particle has mass $0.50\,\mathrm{kg}$, its acceleration $a=-2000/0.50\,\mathrm{m/s^2}=-4000\,\mathrm{m/s^2}$.

Thus, the answer is E.