Problem $1.$ With a time$-$varying current $i(t)$ impressed across the terminals of an inductor $($see Fig. $1,$ also illustrated with plot shown in Fig. $2)$ defined as

$i(t)=\{\begin{array}{cc}0,& t0\\ 3{10}^{-3}{t}^{2}A,& 0=2\end{array}$

Compute the voltage $v(t),$

Compute the corresponding power $p(t),$

Derive the energy $w(t)$ stored in the inductor.

Fig. $1.$

Fig. $2.$