The aim of this study is to develop the power model of the relationship between speed and traffic safety. As the inter-urban roads are characterised with heterogeneous traffic, the heterogeneity became the focus of the analysis. The present study analysed the effects of various types of vehicles through a number of speed change combinations and developed six equations: number of fatal accidents, number of fatalities, number of fatal and serious injury accidents, number of fatal or serious injuries, number of injury accidents and number of injured road users. The results indicated that the Power Model showed high predictability of the speed-accident relationship. The models fit the data well with Rsq in the range of 0.6-0.8. The vehicle category-specific ratio power models exhibited how traffic heterogeneity accounts for traffic safety. The equations' power varies with the types of vehicles, indicating the different sensitivity of accidents and casualties to the speed ratios. Overall, with the power estimates around one, except for all injured victims, the estimates were systematically smaller than those that were initially inferred in Nilsson's Power model. The values indicated that the increase in speed determined the increase in the number of accidents and casualties from year to year. The present study successfully developed the first speed-traffic safety Power Model for Indonesia. As it is exclusively dependent on the speed changes, the model can well describe the direction of change in traffic safety irrespective of other changes in the driving environment factors. © 2021 Institut za Istrazivanja. All rights reserved.