A particle moves along a curvilinear trajectory shown in Fig. When passing through the point O has a 3.6m/sec speed and slows down so that it passes through point A does so with a speed of 1.8m/sec. The distance from point A to point O measured along the path is 5.4meters and the acceleration is proportional to the distance of the particle to point O. Determine the radius of curvature of the path in A if we know that the total acceleration the particle when pass through this point is $\displaystyle\frac{3m}{sec^2}$.