**Question T77:** What is the speed of a particle if the kinetic energy is equal to the rest energy?This question is designed for educational purposes and is aimed at helping students understand the relationship between kinetic energy and rest energy in the context of special relativity. There are no graphs or diagrams accompanying the text.

(a)The expression of kinetic energy is given by,...…(1)Here, m is the mass of the particle, c is the…

Answered: T77. What is the speed of a particle if…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Step 1: Writing the formulas

(a)

The expression of kinetic energy is given by,

$E subscript k equals m c squared open parentheses fraction numerator 1 over denominator square root of 1 minus v squared over c squared end root end fraction minus 1 close parentheses$ ...…(1)

Here, m is the mass of the particle, c is the speed of light and v is the speed of the particle.

The particle's kinetic energy is equal to its rest energy that is $E subscript k equals m c squared$ .

Substituted the values in the equation (1).

$table row cell m c squared end cell equals cell m c squared open parentheses fraction numerator 1 over denominator square root of 1 minus v squared over c squared end root end fraction minus 1 close parentheses end cell row cell open parentheses fraction numerator 1 over denominator square root of 1 minus v squared over c squared end root end fraction minus 1 close parentheses end cell equals 1 row cell fraction numerator 1 over denominator square root of 1 minus v squared over c squared end root end fraction end cell equals 2 end table$

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