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
$2t(a + b)$
$2t\sqrt {({a^2} - {b^2})} $
$t\,\sqrt {{a^2} + {b^2}} $
$2t\sqrt {({a^2} + {b^2})} $
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
Velocity along $X-$axis ${v_x} = \frac{{dx}}{{dt}} = 2at$
Velocity along $Y-$axis ${v_y} = \frac{{dy}}{{dt}} = 2bt$
Magnitude of velocity of the particle,
$v = \sqrt {v_x^2 + v_y^2} = 2t\sqrt {{a^2} + {b^2}} $
Velocity along $Y-$axis ${v_y} = \frac{{dy}}{{dt}} = 2bt$
Magnitude of velocity of the particle,
$v = \sqrt {v_x^2 + v_y^2} = 2t\sqrt {{a^2} + {b^2}} $
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