A particle is moving in one dimension (along x-axis) under the action of a variable force. It's initial position was 16 m right of origin. The variation of its position (x) with time (t) is given as , where x is in m and t in s. The velocity of the partic

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Solution

Q.
A particle is moving in one dimension (along x-axis) under the action of a variable force. It's initial position was 16 m right of origin. The variation of its position (x) with time (t) is given as $x = - 3 t^{3} + 18 t^{2} + 16 t,$ where x is in m and t in s. The velocity of the particle when its acceleration becomes zero is _____ m/s. [2024]

Ans.
(52)    $x = 3 t^{3} + 18 t^{2} + 16 t$

   $v = - 9 t^{2} + 36 t + 16$

   $a = - 18 t + 36$

   $a = 0$ at $t = 2$ $s$

   $v = - 9 {(2)}^{2} + 36 \times 2 + 16$

   $v = 52 m / s$

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