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Question: Answered & Verified by Expert
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?
PhysicsMotion In One DimensionJEE Main
Solution:
2181 Upvotes Verified Answer
The correct answer is: 54

Let us first find speed.

Speed,  v=dxdt=ddt(9t2t3)=18t3t2

For maximum speed, using  dvdt=0

 dvdt=0186t=0t=3 ,

Now finding displacement at that time, we have :

 xmax=8127=54 m

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