Effectively modeling the acceleration behavior of vehicles is an important consideration in a variety of transportation engineering applications. The acceleration profiles of vehicles are important in the geometric design of roadways and are used to model vehicle behavior in simulation software packages. The acceleration profile of the vehicle is also a critical parameter in fuel consumption and emissions models. This paper develops and validates a vehicle dynamics model to predict the maximum acceleration rates of passenger vehicles. The model is shown to be superior to other similar models in that it accurately predicts speed and acceleration profiles in all domains and for a variety of vehicle types. The paper also modifies the model by introducing a reduction factor, which enables the model to predict the typical acceleration patterns for different driver types. The reduction factors for the driving population are shown to follow a normal distribution with a mean of 0.60 and a standard deviation of 0.08. The paper also provides new data sets containing maximum and typical acceleration profiles for thirteen different vehicles and twenty different drivers.