The co-ordinates of a moving particle at any time t are given by $\mathrm{x}={\mathrm{\alpha t}}^3\text{ and }\mathrm{y}={\mathrm{\beta t}}^3$. The speed of the particle at time t is given by :

• A

  $\sqrt{{\mathrm{\alpha }}^2+{\mathrm{\beta }}^2}$

• B

  ${\mathrm{t}}^2\sqrt{{\mathrm{\alpha }}^2+{\mathrm{\beta }}^2}$

• C

  $3\mathrm{t}\sqrt{{\mathrm{\alpha }}^2+{\mathrm{\beta }}^2}$

• D

  $3{\mathrm{t}}^2\sqrt{{\mathrm{\alpha }}^2+{\mathrm{\beta }}^2}$