A small brick is squeezed between two parallel planes in zero-gravity. The planes are perpendicular to the axis $z$. The lower plane always stays in rest, whilst the upper one is moving with the constant velocity $\vec{v}$ along the axis $x$, see the figure. Initially the velocity of the brick $\vec{u}_0$ is perpendicular to $\vec{v}$ and lies in axis $y$. The friction between the planes and the brick is dry with the same coefficient of kinetic friction.

1 Given the initial acceleration of the brick $a_0$, find the displacement $l_y$ of the brick along the axis $y$ after a long time.

2 Obtain an expression of $l_y$ for arbitrary speeds $v$ and $u_0$, and evaluate the answer for $v=u_0=1~\mathrm{m}/\mathrm{s}$, and $a_0=1~\mathrm{m}/\mathrm{s}^2$ with four digits.