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NEET 2006 (AIPMT) · Velocity, Acceleration & Variable Motion

Velocity, Acceleration & Variable Motion question from NEET 2006 (AIPMT)

Q42NEET 2006 · AIPMTMedium

Velocity, Acceleration & Variable Motion

A particle moves along a straight line OX. At a time t (in seconds) the distance x (in metres) of the particle from O is given by x = 40 + 12t $-$ t3. How long would the particle travel before coming to rest?

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Answer: (a)

$v = \dfrac{dx}{dt} = 12 - 3t^2 = 0 \Rightarrow t = 2\text{ s}$
$x(0) = 40\text{ m}$ , $x(2) = 40 + 24 - 8 = 56\text{ m}$
$v > 0$ throughout, so distance $= 56 - 40 = 16\text{ m}$
So the answer is (a) 16 m.

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