A solid horizontal surface is covered with a thin layer of oil. A rectangular block of mass $m=0.4kg$ is at rest on this surface. An impulse of $1.0Ns$ is applied to the block at time $t=0$ so that it starts moving along the $x$-axis with a velocity $$v\left( t \right) = {v_0}{e^{ - t/\tau }},$$ where ${v_0}$ is a constant and $\tau = 4s.$ The displacement of the block, in metres, at $t = \tau$ is $\underline{\hspace{2cm}}$ Take ${e^{ - 1}} = 0.37.$