A particle of mass $$m$$ moves in a straight line under the influence of a certain force such that the power $$P$$ delivered to it remains constant. Starting from rest, the straight line distance traveled by the moving particle in time $$t$$ is

A

$$\left(\frac{8Pt^3}{27m}\right)^{1/2}$$

B

$$\left(\frac{4Pt^3}{27m}\right)^{1/2}$$

C

$$\left(\frac{8Pt^2}{9m}\right)^{1/2}$$

D

$$\left(\frac{8Pt^3}{9m}\right)^{1/2}$$