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General
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Question

If the velocity of particle is given by v equals open parentheses 180 minus 16 x close parentheses to the power of 1 divided by 2 end exponent blank m divided by s, then its acceleration will be

  1. Zero  
  2. 8 blank m divided by s to the power of 2 end exponent  
  3. negative 8 blank m divided by s to the power of 2 end exponent  
  4. 4 blank m divided by s to the power of 2 end exponent  

The correct answer is: negative 8 blank m divided by s to the power of 2 end exponent


    v equals open parentheses 180 minus 16 x close parentheses to the power of 1 divided by 2 end exponent
    As a equals fraction numerator d v over denominator d t end fraction equals fraction numerator d v over denominator d x end fraction. fraction numerator d x over denominator d t end fraction
    therefore a equals fraction numerator 1 over denominator 2 end fraction open parentheses 180 minus 16 x close parentheses to the power of negative 1 divided by 2 end exponent cross times left parenthesis negative 16 right parenthesis open parentheses fraction numerator d x over denominator d t end fraction close parentheses
    equals negative 8 open parentheses 180 minus 16 x close parentheses to the power of negative 1 divided by 2 end exponent cross times v
    equals negative 8 open parentheses 180 minus 16 x close parentheses to the power of negative 1 divided by 2 end exponent cross times open parentheses 180 minus 16 x close parentheses to the power of 1 divided by 2 end exponent equals negative 8 blank m divided by s to the power of 2 end exponent

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