In traffic accident analysis, vehicle speed estimation is crucial for determining accident causation and establishing legal liability. Although cross-ratio-based methods are widely employed in traffic accident video analysis, they remain primarily limited to average speed calculations on straight road sections. This study proposes a video-based speed estimation technique applicable to curved roads by integrating cross-ratio geometric principles with vehicle dynamics. The proposed method estimates continuous speed variations from video data through automatic selection of reliable frame combinations. Accuracy is further enhanced by incorporating vehicle dynamics principles specific to curved driving scenarios. The method was validated through comparative analyses with existing approaches, employing PC-Crash simulations and real accident cases. Experimental results demonstrate that the proposed method improves speed estimation accuracy on curved roads and during acceleration or deceleration. The method also proves effective for the temporal analysis of event data recorder (EDR) data in multiple-collision accidents. This video-based approach is expected to enhance the reliability and objectivity of traffic surveillance video analysis, particularly for application as legal evidence.