A charged particle of mass m and charge q is released from...

A charged particle of mass $m$ and charge $q$ is released from rest in an electric field of constant magnitude $E$. The kinetic energy of the particle after a time $t$ is (A) $\frac{E^{2} q^{2} t^{2}}{m}$ (B) $\frac{2 E^{2} q^{2} t^{2}}{m}$ (C) $\frac{E^{2} q^{2} t^{2}}{2 m}$ (D) $\frac{4 E^{2} q^{2} t^{2}}{m}$

A charged particle of mass $m$ and charge $q$ is released from rest in an electric field of constant magnitude $E$. The kinetic energy of the particle after a time $t$ is
(A) $\frac{E^{2} q^{2} t^{2}}{m}$
(B) $\frac{2 E^{2} q^{2} t^{2}}{m}$
(C) $\frac{E^{2} q^{2} t^{2}}{2 m}$
(D) $\frac{4 E^{2} q^{2} t^{2}}{m}$

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Key Concepts

Equations of Motion in Constant Acceleration

For a particle starting from rest and subject to constant acceleration, the velocity after time t can be computed using v = at. This concept is critical when calculating the kinetic energy of the particle as it describes how the velocity evolves over time.

Kinetic Energy

The kinetic energy of a particle is given by K = 1/2 mv^2. When the velocity is expressed in terms of acceleration and time, as derived from the equations of motion, this formulation allows for directly relating the kinetic energy to the electric field, charge, mass, and time.

Electric Force

The electric force on a charged particle is determined by the product of the charge and the electric field. This force, given by F = qE, acts on the particle, causing it to accelerate, and is central to understanding how particles behave in an electric field.

Newton's Second Law

Newton's second law, F = ma, connects the force acting on a particle to its acceleration. When the only force is the electric force, the particle's acceleration is given by a = qE/m, linking the charge, electric field, and mass of the particle.

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