The displacement 'x' (in meter) of a particle of mass 'm' (in kg) moving in one dimension under the action of a force, is related to time 't' (in sec) by t = √(x) + 3. The displacement of the particle when its velocity is zero, will be (a) 4 m (b) 0 m (zero) (c) 6 m (d) 2 m

Answer: (b). √(x) = t - 3 ⇒ x = (t - 3)² v = dx/dt = 2(t - 3) = 0 ⇒ t = 3 s x(3) = 0 So the answer is (b) 0 m.

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Q35NEET 2013Medium

Velocity, Acceleration & Variable Motion

The displacement 'x' (in meter) of a particle of mass 'm' (in kg) moving in one dimension under the action of a force, is related to time 't' (in sec) by t = $\sqrt{x} + 3$ . The displacement of the particle when its velocity is zero, will be

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Answer: (b)

$\sqrt{x} = t - 3 \Rightarrow x = (t - 3)^2$
$v = \dfrac{dx}{dt} = 2(t - 3) = 0 \Rightarrow t = 3\text{ s}$
$x(3) = 0$
So the answer is (b) 0 m.

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