A proton is either released at rest or launched with a certain velocity in a uniform electric field. Which of the graphs in figure could possibly show how the kinetic energy of the proton changes during the proton's motion?

Engineering

Physics

Acceleration

Electric Flux and Gauss Law and its Applications

Electric Potential Energy and Electric Potential

Question

A proton is either released at rest or launched with a certain velocity in a uniform electric field. Which of the graphs in figure could possibly show how the kinetic energy of the proton changes during the proton's motion?

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A proton in a uniform electric field experiences constant force F = qE, so constant acceleration a = qE/m. Kinetic energy KE = (1/2)mv². If released from rest (initial KE=0), KE increases quadratically with time since v = at, so KE = (1/2)m(a²t²) ∝ t². If launched with initial velocity, KE still increases quadratically. The graph must be a parabola opening upwards, starting from zero or positive value.

Equation: $K E = \frac{1}{2} m v^{2} = \frac{1}{2} m {(a t + v_{0})}^{2}$

Final answer: The correct graph is the one showing a parabolic increase (upward opening curve), which is the first image (top-left).