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

2 t (a + b)

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

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

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

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Solution

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

$r =^i a t^{2} +^j b t^{2}, V = \frac{d r}{d t} =^i 2 a t +^j 2 b t$
  $∴$ Magnitude of $v = \sqrt{(4 a^{2} t^{2} + 4 b^{2} t^{2})}$

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

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Similar questions

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

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