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NEET 2007 (AIPMT) · Velocity, Acceleration & Variable Motion

Velocity, Acceleration & Variable Motion question from NEET 2007 (AIPMT)

Q40NEET 2007 · AIPMTMedium

Velocity, Acceleration & Variable Motion

The position 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?

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Answer: (a)

$v = \dfrac{dx}{dt} = 18t - 3t^2$
Speed is maximum when $a = \dfrac{dv}{dt} = 18 - 6t = 0 \Rightarrow t = 3\text{ s}$
$x(3) = 9(9) - 27 = 54\text{ m}$
So the answer is (a) 54 m.

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