The coordinates of a moving particle at any t | vedclass

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(D) The velocity component along the $X$-axis is given by $v_x = \frac{dx}{dt} = \frac{d}{dt}(at^2) = 2at$. The velocity component along the $Y$-axis

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

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(D) The velocity component along the $X$-axis is given by $v_x = \frac{dx}{dt} = \frac{d}{dt}(at^2) = 2at$. The velocity component along the $Y$-axis is given by $v_y = \frac{dy}{dt} = \frac{d}{dt}(bt^2) = 2bt$. The magnitude of the velocity (speed) of the particle is $v = \sqrt{v_x^2 + v_y^2}$. Substituting the values,we get $v = \sqrt{(2at)^2 + (2bt)^2} = \sqrt{4a^2t^2 + 4b^2t^2} = \sqrt{4t^2(a^2 + b^2)}$. Simplifying this,we get $v = 2t\sqrt{a^2 + b^2}$.

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

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