In a cathode ray tube, clectrons initially at rest are...

In a cathode ray tube, clectrons initially at rest are accelerated by a uniform electric ficld of magnitude $4.0 \times 10^{5} \mathrm{N} / \mathrm{C}$ during the first $5.0 \mathrm{cm}$ of the tube's length; then they move at essentially constant velocity another $45 \mathrm{cm}$ before hitting the screen. (a) Find the speed of the electrons when they hit the screen. (b) How long does it take them to travel the length of the tube?

In a cathode ray tube, clectrons initially at rest are accelerated by a uniform electric ficld of magnitude $4.0 \times 10^{5} \mathrm{N} / \mathrm{C}$ during the first $5.0 \mathrm{cm}$ of the tube's length; then they move at essentially constant velocity another $45 \mathrm{cm}$ before hitting the screen.
(a) Find the speed of the electrons when they hit the screen.
(b) How long does it take them to travel the length of the tube?

Key Concepts

Uniform Electric Field

A uniform electric field is a region in which the electric force experienced by a charged particle is constant in magnitude and direction. This concept is crucial because it provides a predictable, steady acceleration when a charged particle, such as an electron, enters the field, which is given by F = qE.

Newton's Second Law

Newton's second law, expressed as F = ma, links the force acting on an object to its mass and the acceleration it experiences. This principle is essential for determining the acceleration of a charged particle when it is subjected to an electric force.

Kinematics with Constant Acceleration

Kinematics under constant acceleration uses equations that relate displacement, velocity, acceleration, and time. These equations allow us to calculate the final velocity of a particle starting from rest over a given distance, as well as the time taken to traverse that distance during the acceleration phase.

Uniform Motion

Uniform motion describes the motion of an object traveling at a constant velocity, meaning that no net acceleration occurs. In the context of the problem, after the initial acceleration phase, the particle moves at a constant speed, and this concept is used to determine the time taken to cover the remaining distance.

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