Answer
(a)
$$
\begin{array}{c}{\mathrm{Q}=864 \mathrm{C}}\end{array}
$$
---
(b)
$$\mathrm{Energy} =1,167 J$$
Work Step by Step
(a)
$40 m A=0.04 A$
$Q=$ area under the current-time curve $=\int I d t=(0.04)(6)(3600)=864 \mathrm{C}$
$$
\begin{array}{c}{\mathrm{Q}=864 \mathrm{C}}\end{array}
$$
---
(b)
$$\quad \frac{\mathrm{d} \mathrm{w}}{\mathrm{dt}}=\mathrm{P}$$
$$w=\int P d t=\int v i d t=(3600) \int_{0}^{2} v i d t+(3600) \int_{2}^{6} v i d t$$
$$=(3600) \int_{0}^{2}\left(1.2-0.45 e^{-t / 0.4}\right)(0.04) d t+(3600) \int_{2}^{6}\left(1.5-0.3 e^{-(t-2) / 0.4}\right)(0.04) d t$$
$$=1,167 J$$
$$\therefore \mathrm{Energy} =1,167 J$$
