JEE Advanced 2018 · Paper 2, Physics question 7

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