Physics-
General
Easy

Question

A particle moves along a straight line O X. At a time t (in seconds) the distance x (in metres) of the particle from O is given by x equals 40 plus 12 t minus t to the power of 3 end exponent
How long would the particle travel before coming to rest

  1. 24 blank m  
  2. 40 blank m  
  3. 56 blank m  
  4. 16 blank m  

The correct answer is: 56 blank m


    Distance travelled by the particle is
    x equals 40 plus 12 t minus t to the power of 3 end exponent
    We know that, speed is rate of change of distance i.e.
    v equals fraction numerator d x over denominator d t end fraction
    therefore v equals fraction numerator d over denominator d t end fraction open parentheses 40 plus 12 t minus t to the power of 3 end exponent close parentheses equals 0 plus 12 minus 3 t to the power of 2 end exponent
    But final velocity v equals 0
    therefore 12 minus 3 t to the power of 2 end exponent equals 0
    rightwards double arrow t to the power of 2 end exponent equals fraction numerator 12 over denominator 3 end fraction equals 4 rightwards double arrow t equals 2 s
    Hence, distance travelled by the particle before coming to rest is given by
    x equals 40 plus 12 open parentheses 2 close parentheses minus open parentheses 2 close parentheses to the power of 3 end exponent equals 40 plus 24 minus 8 equals 64 minus 8 equals 56 m

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