A proton accelerates from rest in a uniform electric field of 640 N / C. At some time later, its

step 1 Question number 58, for the first part, the acceleration of the proton is equal to the force on

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 time later, its speed is $1.20 \times 10^{6} \mathrm{m} / \mathrm{s}$ a. What is the magnitude of 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 interval? d. What is its kinetic energy at the later time?

A proton accelerates from rest in a uniform electric field of $640 \mathrm{N} / \mathrm{C}$. At some time later, its speed is $1.20 \times 10^{6} \mathrm{m} / \mathrm{s}$
a. What is the magnitude of 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 interval?
d. What is its kinetic energy at the later time?

Key Concepts

Kinetic Energy

Kinetic energy quantifies the energy an object possesses due to its motion and is given by the expression KE = ½ mv², where m is the mass and v is the velocity of the object. This concept is crucial in understanding energy transfer and conversion when a particle accelerates, and it plays an important role in energy conservation analyses.

Kinematics of Constant Acceleration

Kinematic equations describe the motion of objects under constant acceleration by relating displacement, velocity, acceleration, and time. These equations are used to calculate variables such as time taken to reach a certain velocity and the distance traveled under uniform acceleration, which are key in analyzing motion in problems involving constant forces.

Electric Field and Force

An electric field is a region in space where a charged particle experiences a force, which is calculated using the relation F = qE, where q represents the charge and E represents the electric field strength. This concept is fundamental in understanding how charged particles interact with fields and is critical for determining the motion of the particle under the influence of the field.

Newton's Second Law

Newton's second law of motion states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). This principle is essential for linking the electric force acting on a charged particle to the resulting acceleration, thereby allowing one to determine how quickly the particle's velocity changes under the influence of that force.

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