Problem $2.$ The voltage pulse described by the following equations is impressed across the terminals of $0\mathrm{.}5F$ capacitor:

$v(t)=\{\begin{array}{cc}0,& t0\\ 4tV,& 0t1\\ 4e^{-(t-1)}V,& 1t\end{array}$

Derive the expression for the capacitor current, power, and energy.

Sketch the voltage, current, power, and energy as function of time. Line up plots vertically.

Specify the interval of time when energy is being stored in the capacitor.

Specify the interval of time when energy is being delivered by the capacitor.

Evaluate the integrals ${\displaystyle \underset{0}{\overset{1}{}}}pdt$ and ${\displaystyle \underset{1}{\overset{}{}}}pdt$ and comment on their significance.