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NTA Abhyas JEE Main2020PhysicsMotion in One DimensionPractice

The position x of a particle with respect to time t along the x -axis is given by x = 9 t 2 − t 3 where x is in metres and t in second. What will be the position of this particle (in m ) when it achieves maximum speed along the positive x - direction?

Correct answer

54

Step-by-step solution

Let us first find speed. Speed, v = d x d t = d d t ( 9 t 2 − t 3 ) = 18 t − 3 t 2 For maximum speed, using d v d t = 0 d v d t = 0 ⇒ 18 − 6 t = 0 ⇒ t = 3 , Now finding displacement at that time, we have : ⇒ x max = 81 − 27 = 54 m

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