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Motion in A Straight Line question

2007 · Q131
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Motion in A Straight Line question

2007 · Q131

NEETPhysicsMotion in A Straight LineMCQ+4 / −1
The positions x of a particle with respect to time t along x-axis is given by x = 9t2 −-− t3 where x is in metres and t in seconds. What will be the position of this particle when it achieves maximum speed along the + x direction ?
  1. A
    54 m
  2. B
    81 m
  3. C
    24 m
  4. D
    32 m
View written solutionFree

Correct answer: A

Speed v = dxdt{{dx} \over {dt}}dtdx​ = ddt(9t2−t3){d \over {dt}}\left( {9{t^2} - {t^3}} \right)dtd​(9t2−t3) = 18t - 3t2

At maximum speed

dvdt{{dv} \over {dt}}dtdv​ = 0

⇒\Rightarrow⇒ 18 - 6t = 0

⇒\Rightarrow⇒ t = 3

∴\therefore∴ Position of the particle = 81 - 27 = 54 m

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