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The models based on vehicle speed have been used to estimate fuel consumption and CO2 emissions. However, these models could not properly estimate the change in fuel consumption and CO2 emissions as the speed changes. As for the alternative method, people try to consider using acceleration instead of speed. Although acceleration has been seriously considered, determining critical aggressive acceleration value in relation to fuel consumption and CO2 emissions is difficult to find. In this study, evaluation models of fuel consumption were developed using instantaneous acceleration, and we defined the critical aggressive acceleration values for different states of the vehicle from the viewpoints of fuel consumption and emissions. We used a mid-sized Liquefied Petroleum Gas (LPG) passenger car and obtained instantaneous data from a digital tachograph installed in the car while it accelerates. We developed two fuel consumption models and found critical aggressive accelerations, respectively: a model of starting vehicle that measures range of speed required to overcome the inertia during acceleration from stop state, and the other model for the driving state. We used Classification and Regression Tree (CART) analysis to find the critical aggressive accelerations at which the increments of fuel consumption change abruptly. As a result, the critical aggressive accelerations causing abrupt change in the increments of fuel consumption were found to be 2.598 m/s2 for the starting of vehicles and 1.4705 m/s2 when driving them. We also found that the increments of fuel consumption can be explained through quadratic and exponential functions with instantaneous acceleration. [ABSTRACT FROM AUTHOR]