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The coordinates of a moving particle at any time ' \( t \) ' are given by \( x=\alpha t^{3} \) and \( y=\beta t^{3} \). The speed of the particle at time ' \( t \) ' is given by
[Similar DPMT 1984; CPMT 1997; AIEEE 2003]
(a) \( \sqrt{\alpha^{2}+\beta^{2}} \)
(b) \( 3 t \sqrt{\alpha^{2}+\beta^{2}} \)
(c) \( 3 t^{2} \sqrt{\alpha^{2}+\beta^{2}} \)
(d) \( t^{2} \sqrt{\alpha^{2}+\beta^{2}} \)
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