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JEE Main20241 Feb 2024Morning ShiftPhysicsMotion in One DimensionActual

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 is in s . The velocity of the particle when its acceleration becomes zero is _________ m s - 1 .

Correct answer

0

Step-by-step solution

Given: x = - 3 t 3 + 18 t 2 + 16 t As we know, v = d x d t = - 9 t 2 + 36 t + 16 Now, a = d v d t = - 18 t + 36 For a = 0 , time till be t = 2 s Therefore, required velocity v = - 9 ( 2 ) 2 + 36 × 2 + 16 v = 52 m s - 1

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