A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity 'v' that varies as v = α√(x). The displacement of the particle varies with time as (a) t2 (b) t (c) t1/2 (d) t3

Answer: (a). (dx)/(√(x)) = α dt ⇒ 2√(x) = α t x = (α² t²)/(4) So x ∝ t²; the answer is (a).

A particle located at x = 0 at time t = 0, starts moving along the… | JEE Main 2006 (AIEEE)

Q43JEE Main 2006 · AIEEEMedium

Velocity, Acceleration & Variable Motion

A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity 'v' that varies as $v = \alpha\sqrt{x}$ . The displacement of the particle varies with time as

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Answer: (a)

$\dfrac{dx}{\sqrt{x}} = \alpha\,dt \Rightarrow 2\sqrt{x} = \alpha t$
$x = \dfrac{\alpha^2 t^2}{4}$
So $x \propto t^2$ ; the answer is (a).

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