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Question

The acceleration a of a particle starting from rest varies with time according to relation a equals alpha t plus beta. The velocity of the particle after a time t will be

  1. fraction numerator alpha t to the power of 2 end exponent over denominator 2 end fraction plus beta  
  2. fraction numerator alpha t to the power of 2 end exponent over denominator 2 end fraction plus beta t  
  3. alpha t to the power of 2 end exponent plus fraction numerator 1 over denominator 2 end fraction beta t  
  4. fraction numerator open parentheses alpha t to the power of 2 end exponent plus blank beta close parentheses over denominator 2 end fraction  

The correct answer is: fraction numerator alpha t to the power of 2 end exponent over denominator 2 end fraction plus beta t


    Given, a equals alpha t plus beta
    fraction numerator d v over denominator d t end fraction equals blank alpha t plus beta
    not stretchy integral subscript 0 end subscript superscript t end superscript d v equals not stretchy integral subscript 0 end subscript superscript t end superscript alpha t d t plus not stretchy integral subscript 0 end subscript superscript t end superscript beta d t
    v equals fraction numerator alpha t to the power of 2 end exponent over denominator 2 end fraction plus beta t

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