Maths-
SAT
Easy

Question

L equals S square root of 1 minus v squared over c squared end root
When the speed of an object approaches the speed of light, its length as seen by an observer changes. When the object is stationary relative to an observer, its length is S, and when the same object is moving at speed v relative to the observer, its length is L. The formula above expresses L in terms of S, v, and c, the speed of light. Which of the following gives the speed of the object in terms of the other quantities? 

  1. nu equals c square root of 1 minus L squared over s squared end root
  2. v equals c square root of 1 plus L squared over S squared end root
  3. v equals c squared open parentheses 1 minus L squared over S squared close parentheses
  4. v equals c squared open parentheses 1 plus L squared over s squared close parentheses

The correct answer is: nu equals c square root of 1 minus L squared over s squared end root


    L equals S square root of 1 minus v squared over c squared end root
    L over S equals square root of 1 minus v squared over c squared end root
    L squared over S squared equals 1 minus V squared over C squared
    V squared over C squared equals 1 minus L squared over S squared
    V squared equals C squared open parentheses 1 minus L squared over S squared close parentheses
    V equals square root of C squared open parentheses 1 minus L squared over S squared close parentheses end root
    V equals C square root of 1 minus L squared over S squared end root

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