The coordinates of a moving particle at any time ?t? are given by x = at3 and y = bt3. The speed of the particle at time ?t? is given by [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.                      \[{{t}^{2}}\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}\]