Evaluating the validity of an existing user performance model in a variety of tasks is important for enhancing its applicability. The model studied in this work is the steering law for predicting the speed and time needed to perform tasks in which a cursor or a car passes through a constrained path. Previous HCI studies have refined this model to take additional path factors into account, but its applicability has only been evaluated in GUI-based environments such as those using mice or pen tablets. Accordingly, we conducted a user experiment with a driving simulator to measure the speed and time on curved roads and thus facilitate evaluation of models for pen-based path-steering tasks. The results showed that the best-fit models for speed and time had adjusted r^2 values of 0.9342 and 0.9723, respectively, for three road widths and eight curvature radii. While the models required some adjustments, the overall components of the tested models were consistent with those in previous pen-based experimental results. Our results demonstrated that user experiments to validate potential models based on pen-based tasks are effective as a pilot approach for driving tasks with more complex road conditions.