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COMEDK2019MathematicsApplication of Derivatives

A stone is thrown vertically upwards and the height x f t. reached by the stone in t sec is given by x=80 t-16 t² . The stone reaches the maximum height in

Options

  1. A2 sec
  2. B2.5 sec
  3. C3 sec
  4. D1.5 sec

Correct answer

B. 2.5 sec

Step-by-step solution

We have, aligned x &=80 t-16 t² d x d i &=80-32 t aligned For maximum value of x , aligned d x d t &=0 80-32 t &=0 t= 80 32 =2.5 aligned Again, d² x d t² =-32 < 0 So, at t=25 sec , x is maximum.

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