A solid horizontal surface is covered with a thin layer of oil. A...

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 $v\left(t\right) = {v}_{0}{e}^{- \dfrac{t}{τ}}$ , where ${v}_{0}$ is a constant and $τ = 4$ . The displacement of the block, in meter, at $t = τ$ is __________. Take ${e}^{- 1} = 0.37$