Given, $I = {t^2}{e^{ - t}}$

So, ${{dI} \over {dt}} = 2t{e^{ - t}} - {t^2}{e^{ - t}}$

$\left| \varepsilon \right| = L{{dI} \over {dt}}$

here emf is zero when ${{dI} \over {dt}}$ = 0

$\therefore$ $2t{e^{ - t}} - {t^2}{e^{ - t}}$ = 0

$\Rightarrow$ $2t{e^{ - t}} = {t^2}{e^{ - t}}$

$\Rightarrow$ $t{e^{ - t}}\left( {t - 2} \right)$ = 0

As t $\ne$ $\infty$, t $\ne$ 0

$\therefore$ t = 2 sec