Physics-
General
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Question

A particle located at x equals 0 at time t equals 0, starts moving along the positive x-direction with a velocity ‘v’ that varies as v equals a square root of x. The displacement of the particle varies with time as

  1. t  
  2. t to the power of 1 divided by 2 end exponent  
  3. t to the power of 3 end exponent  
  4. t to the power of 2 end exponent  

The correct answer is: t to the power of 2 end exponent


    v equals alpha square root of x rightwards double arrow fraction numerator d x over denominator d t end fraction equals proportional to square root of x rightwards double arrow fraction numerator d x over denominator square root of x end fraction equals alpha d t
    By integrating both sides not stretchy integral x to the power of negative 1 divided by 2 end exponent d x equals not stretchy integral alpha blank d t
    rightwards double arrow fraction numerator square root of x over denominator 1 divided by 2 end fraction equals alpha t rightwards double arrow square root of x equals fraction numerator 1 over denominator 2 end fraction alpha t rightwards double arrow x equals fraction numerator 1 over denominator 4 end fraction alpha to the power of 2 end exponent t to the power of 2 end exponent blank therefore x proportional to t to the power of 2 end exponent

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