Speed of a Particle with Constant Total Energy – Rankers Physics

Potential Energy & Equilibrium: Practice Problem & Solution

A particle with constant total energy \( E \) moves in one dimension in a region where the potential energy is represented by \( U(x) \). The speed of the particle is zero where:
\( \frac{d^2U(x)}{dx^2} = 0 \)
\( \frac{dU(x)}{dx} = 0 \)
\( U(x) = E \)
\( U(x) = 0 \)

Solution Explained:

To solve this problem, we apply the core principles of Potential Energy & Equilibrium. Understanding the underlying formula is key to arriving at the correct answer below:

Total mechanical energy of a particle is the sum of its kinetic energy and potential energy: \( E = K + U(x) \). When the speed of the particle is zero, its kinetic energy \( K = 0 \), which gives \( E = U(x) \).

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