Installation of a large-capacity battery pack is a straightforward method to extend the range of battery electric vehicles (BEV or all-electric vehicles). However, at the same time, a large-capacity battery pack not only occupies a big space but also significantly increases the vehicle weight, which directly impacts the fuel economy and vehicle performance. This implies that increasing the battery capacity has an obvious limitation in extending the EV range. In this paper, we introduce a system-level framework to extend the range of BEV with the consideration of the vehicle dynamics, electric powertrain characteristics, road slopes, payload, and regenerative braking. This paper particularly takes into account driving time so that the resultant BEV power management does not impractically slow down the vehicle velocity. The BEV power management framework derives energy-aware velocity planning, i.e., a desirable instantaneous velocity at each distance step (or at each time instant). The major technical contributions of this paper compared with the previous work include: 1) practically applicable velocity planning for production BEVs from superb BEV power model fidelity; 2) new performance metrics to consider both driving energy and driving time: energy-delay product (EDP), energy-square-delay product, and energy-cubic-delay product; 3) heuristics to derive EDP-aware velocity planning; 4) comparative analysis of the velocity planning between BEV and internal combustion engine vehicles; and 5) analysis of the model fidelity impact on the energy-aware velocity planning. The proposed method results in up to a 46.2% improvement of the EDP compared with the least-energy constant velocity driving.