In a 100-m linear accelerator, an electron is accelerated to...

In a $100-\mathrm{m}$ linear accelerator, an electron is accelerated to $1.00 \%$ of the speed of light in $40.0 \mathrm{m}$ before it coasts for $60.0 \mathrm{m}$ to a target. (a) What is the electron's acceleration during the first $40.0 \mathrm{m} ?$ (b) How long does the total flight take?

Key Concepts

Acceleration and Velocity Relationship

This key concept involves understanding how acceleration is defined as the rate at which velocity changes over time. It explains how, starting from a given initial velocity, an object’s speed increases linearly under constant acceleration until it reaches a new specified speed, and it is fundamental in calculating both the acceleration required to achieve a velocity change and the time taken for that change.

Uniform Motion (Coasting)

Uniform motion describes motion at a constant speed with zero acceleration. When an object moves in this manner, the displacement is simply the product of speed and time. In many problems, the motion is divided into segments where one involves acceleration and the other involves constant velocity, allowing the motion analysis to be separated accordingly.

Understanding Speed as a Fraction of the Speed of Light

While the speed of light is a fundamental constant in physics, expressing an object’s speed as a percentage of the speed of light is useful for judging when relativistic effects might be important. In cases where the object’s speed is a small fraction of the speed of light, classical mechanics can typically be applied without significant error.

Kinematics Equations

These are the mathematical relationships that describe the motion of objects under constant acceleration. They relate displacement, initial velocity, final velocity, acceleration, and time. In problems involving acceleration over a known distance, these equations enable the determination of unknown quantities when certain others are provided.

Constant Acceleration

This concept refers to situations where the acceleration of an object remains uniform over time. In such cases, the standard kinematic formulas for displacement and velocity as functions of time apply, simplifying calculations and making it possible to predict the motion parameters accurately.

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