The increase in vehicle numbers in California, driven by inadequate transportation systems and sparse speed cameras, necessitates effective vehicle speed detection. Detecting vehicle speeds per lane is critical for monitoring High-Occupancy Vehicle (HOV) lane speeds, distinguishing between cars and heavy vehicles with differing speed limits, and enforcing lane restrictions for heavy vehicles. While prior works utilized YOLO (You Only Look Once) for vehicle speed detection, they often lacked accuracy, failed to identify vehicle lanes, and offered limited or less practical classification categories. This study introduces a fine-tuned YOLOv11 model, trained on almost 800 bird's-eye view images, to enhance vehicle speed detection accuracy which is much higher compare to the previous works. The proposed system identifies the lane for each vehicle and classifies vehicles into two categories: cars and heavy vehicles. Designed to meet the specific requirements of traffic monitoring and regulation, the model also evaluates the effects of factors such as drone height, distance of Region of Interest (ROI), and vehicle speed on detection accuracy and speed measurement. Drone footage collected from Northern California was used to assess the proposed system. The fine-tuned YOLOv11 achieved its best performance with a mean absolute error (MAE) of 0.97 mph and mean squared error (MSE) of 0.94 $\text{mph}^2$, demonstrating its efficacy in addressing challenges in vehicle speed detection and classification.