Free-flow movement of vehicles in microsimulation software is usually defined by a set of equations with no explicit link to the instantaneous dynamics of the vehicles. In some cases, the car and the driver are modeled in a deterministic way, producing a driving behavior, which does not resemble real measurements, in terms of car dynamics and driving style. Depending on the research topic, the interest in microsimulation is to capture traffic dynamics phenomena, such as shockwave propagation or hysterisis. Existing car-following models are designed to simulate more the traffic evolution, rather than the vehicle motion, and consequently, minimal computational complexity is a strong requirement. However, traffic-related phenomena, such as the capacity drop are influenced by the free-flow acceleration regime. Furthermore, the acceleration pattern of a vehicle plays an essential role in the estimation of the energy required during its motion, and therefore in the fuel consumption and the CO2 emissions. The present work proposes a lightweight microsimulation free-flow acceleration model (MFC) that is able to capture the vehicle acceleration dynamics accurately and consistently, it provides a link between the model and the driver and can be easily implemented and tested without raising the computational complexity. The proposed model is calibrated, validated and compared with known car-following models on road data on a fixed route inside the Joint Research Centre of the European Commission. Finally, the MFC is assessed based on 0-100km/h acceleration specs of vehicles available in the market. The results prove the robustness and flexibility of the model.