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Easy

Question

The displacement of a particle undergoing rectilinear motion along the x-axis is given by x equals left parenthesis 2 t to the power of 2 end exponent plus 21 t to the power of 2 end exponent plus 60 t plus 6 right parenthesis. The acceleration of the particle when its velocity is zero is

  1. 36 m s to the power of negative 2 end exponent  
  2. 9 m s to the power of negative 2 end exponent  
  3. negative 9 m s to the power of negative 2 end exponent  
  4. negative 18 m s to the power of negative 2 end exponent  

The correct answer is: negative 18 m s to the power of negative 2 end exponent


    x equals 2 t to the power of 3 end exponent plus 21 t to the power of 2 end exponent plus 60 t plus 6
    therefore v equals fraction numerator d x over denominator d t end fraction equals 6 t to the power of 2 end exponent plus 42 t plus 60
    But , v equals 0 (given)
    t to the power of 2 end exponent plus 7 t plus 10 equals 0
    rightwards double arrow blank t equals negative 5s
    or t equals negative 2s
    a equals fraction numerator d v over denominator d t end fraction equals 12 t plus 42
    a blank t equals 5 s equals negative 60 plus 42 equals negative 18 m s to the power of negative 2 end exponent
    a blank t equals 2 s equals negative 24 plus 42 equals 18 m s to the power of negative 2 end exponent

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