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AP EAMCET20226 Jul 2022Evening ShiftMathematicsApplication of DerivativesActual

For a particle moving on a straight line it is observed that the distance, ' s ' at a time ' t ' is given by S=6 t- t^3 2 . The maximum velocity during the motion is

Options

  1. A3
  2. B6
  3. C9
  4. D12

Correct answer

B. 6

Step-by-step solution

aligned V & = d S d t = d d t (6 t- t^3 2 ) V & =6- 3 2 t^2 d V d t =-3 t d V d t & =0 -3 t=0 t & =0 d^2 V d t^2 =-3 < 0 aligned V is maximum at t=0 V=6- 3 2 0=6

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