With energy and environmental issues rising, electric vehicles (EVs) will become an essential mode of transportation in logistics distribution. A vital scenario to consider is the dependence of traffic congestion on vehicle travel times, as it is common in urban areas today. This feature means that the speed of an EV on each route may be distinct during different periods. Because EVs have a limited driving range, various works in the literature have proposed energy consumption models as a function of speed and aerodynamic factors. However, their application remains limited and oversimplified due to their dependence on speed and travel times. In the case of speed, the models in the literature work under an average speed during a given arc or introduce approximations with piece-wise linearization methods. Regarding travel times, current vehicle routing algorithms often reformulate the road network into a complete graph where each arc represents the quickest path between two locations. The results obtained by these methods differ from reality, particularly for Arc Routing Problems involving services on the arcs of a road network. For these reasons, we define the Electric Capacitated Arc Routing Problem with Time-dependent Travel times, and Speed-dependent Energy Consumption Rate (E-TDCARP). Over a planning horizon, each arc is associated with a step-wise speed function. Based on this function, a vehicle s speed can change while traveling on a given arc. The objective is to serve a set of arcs that require services through a fleet of electric vehicles with limited load and battery capacity, minimizing the total travel time. Furthermore, the energy consumption rate per unit of time traveled (ECR) is considered a nonlinear function based on speed. We propose a closed-form energy consumption preprocessing algorithm without approximations. We embed it into an Iterate Local Search metaheuristic (ILS) for E-TDCARP and compare the impact on the design of routes between these alternative vehicles and conventional ones.