A proton accelerates from rest in a uniform electric field...

A proton accelerates from rest in a uniform electric field of $640 \mathrm{~N} / \mathrm{C}$. At some later time, its speed has reached $1.20 \times 10^{6} \mathrm{~m} / \mathrm{s}$ (nonrelativistic, since $v$ is much less than the speed of light). (a) Find the acceleration of the proton. (b) How long does it take the proton to reach this speed? (c) How far has it moved in this time? (d) What is its kinetic energy at this time?

Key Concepts

Kinematics of Constant Acceleration

Kinematic equations describe the motion of objects under constant acceleration. In problems where an object starts from rest, these equations (e.g., v = at and d = ½at²) are used to determine variables like the time taken to reach a certain speed and the distance traveled during that time. These concepts are essential for analyzing linear motion in physics.

Kinetic Energy

Kinetic energy, given by the formula KE = ½mv², represents the energy that an object possesses due to its motion. In the context of charged particles in an electric field, it quantifies the work done on the particle by the force exerted by the field. Understanding kinetic energy is key to linking the particle's acceleration with the energy it gains.

Newton's Second Law

Newton's second law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). This law is crucial when analyzing the motion of particles, as it provides the link between the force exerted by an electric field and the resulting acceleration of the object.

Electric Field and Force

In an electric field, a charged particle experiences a force proportional to the field strength and its charge, given by the relation F = qE. This concept is fundamental in electromagnetism because it explains how electric fields influence the motion of charged particles, such as protons and electrons.

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