A body is projected from origin with a velocity v0 along +ve x-axis on which a force $–\alpha x^2$ is acting on it. Find the maximum distance from origin up to which the body can go. (x is the position of particle).
(1) $\left({3mv_0^2\over2\alpha}\right)^{1\over3}$
(2) $\left({3mv_0^2\over2\alpha}\right)^{1\over2}$
(3) $\left({2mv_0^2\over3\alpha}\right)^{1\over3}$
(4) $\left({2mv_0^2\over3\alpha}\right)^{1\over2}$