With the emergence of urban computing technology, the development of smart cities has gained much attention as a means to improve citizens' quality of life. As traffic accidents constitute a major problem that affects the quality of life, an effective solution to address this problem can significantly increase the level of intelligence of smart cities. This paper presents the development of a mathematical model for accurate analysis of big data to promote the effectiveness of policy decisions, thereby largely advancing the intelligent transportation systems (ITS) of smart cities. Temporal impulse was designed as a novel and measurable quantity to analyze traffic accidents by identifying the hidden patterns, such as varying causes and diverging impacts of traffic accidents. Based on the big data produced by the South Korean National Police Agency, we analyzed traffic accidents over three years by applying the temporal impulse. The research results suggested that the temporal impulse not only helped in identifying the varying influence of weather and driver conditions but also facilitated the establishment of sophisticated policies in the implementation of smart cities with the use of urban computing technology. As presented in the section VII, our simulation outputs indicated that our temporal model was predictive within the parameter space comprising driver's dynamic behaviors, day of the week, and environmental factors including weather, road surface condition, and road type. INDEX TERMS Big data, traffic accident data, intelligent transportation systems, smart city technology, stochastic process, time series, and temporal impulse.