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

• A

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

  $t^2\sqrt{{\alpha }^2+{\beta }^2}$
• C

  $\sqrt{{\alpha }^2+{\beta }^2}$
• Correct answer
  D

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

Hence, the correct answer is option: 'D'.