A particle is moving in xy-plane with a constant speed $v_0$ such that its y displacement is given by $\text{y}=\alpha {\text{e}}^{\text{-}\frac{2{\text{v}}_{\text{x}}}{\sqrt{3}{\text{v}}_0}}\text{,}$ where v_x is component of velocity along the x-axis. If at some instant x component of it velocity is positive and the slope of the tangent on its path is $-\frac{1}{\sqrt{3}}\text{,}$ then the displacement of the particle in y-direction at the instant is