Abstract This paper addresses the vulnerability of vehicular ad hoc networks (VANETs) to malicious attacks, specifically focusing on position falsification attacks. Detecting misbehaving vehicles in VANETs is challenging due to the dynamic nature of the network topology and vehicle mobility. The paper considers five types (constant attack, constant offset attack, random attack, random offset attack, and eventually stop attack) of position falsification attacks with varying traffic and attack densities, considered the most severe attacks in VANETs. To improve the detection of these attacks, a novel travel distance feature and an enhanced two-stage detection approach are proposed for classifying position falsification attacks in VANETs. The approach involves deploying the misbehavior detection system within roadside units (RSUs) by offloading computational work from vehicles (onboard units, or OBUs) to RSUs. The performance of the proposed approach was evaluated against different classifiers, including a wide range of paradigms (KNN, Decision Tree, and Random Forest), using the VeReMi dataset. Experimental results indicate that the proposed method based on Random Forest achieved an accuracy of 99.9% and an F1-Score of 99.9%, which are better not only than those achieved by KNN and Decision Tree but also than the most recent approaches in the literature survey.