Lithium$-$ion batteries are primarily intended for mobile storage of power supplied by large$-$scale wind, solar, and conventional power plants. Several companies are in competition with each other to manufacture and sell such lithium$-$ion batteries. By $2021$ it is expected that yearly production of batteries will reach a storage capacity of $1$ terajoule $({10}^{15}J).$ Tesla manufactures battery electric vehicles $($BEVs$)$ with battery capacities between $250$ and $360$ MJ with a range of up to $100$ km $.$ The current generation of BEVs can recharge their batteries at home or at charging stations at rates up to $7$ kW $.$

a$.$ As an illustration of the challenges involved in large$-$scale adoption of this technology, calculate the charging time for a completely discharged $360-$MJ battery.

b$.$ Pose three scientific questions that will need to be addressed by the design of a transportation system based on BEVs that includes