The coordinates of a moving particle at any time are given by $x = a t^{2}$ and $y = b t^{2}$ . The speed of the particle at any moment is

2t(a + b)

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$2 t \sqrt{(a^{2} - b^{2})}$

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$t \sqrt{(a^{2} + b^{2})}$

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$2 t \sqrt{(a^{2} + b^{2})}$

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Solution

The correct option is D
$2 t \sqrt{(a^{2} + b^{2})}$

Velocity along X-axis $V_{x} = \frac{d x}{d t} = 2 a t$

Velocity along Y-axis $V_{y} = \frac{d y}{d t} = 2 b t$

Magnitude of velocity of the particle,

$v = \sqrt{v_{x}^{2} + v_{y}^{2}} = 2 t \sqrt{a^{2} + b^{2}}$

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