Adaptive cruise control is a first step towards increasingly automated vehicles, and while ACC offers potential benefits to the traffic stream depending on the ACC design, less is known about the impacts that commercially available ACC vehicles have traffic flow. Therefore, it is of interest to reliably model commercial ACC vehicle behavior so as to be able to better understand how ACC vehicles may influence the emergent properties of the traffic flow. In this article, a set of car following experiments are conducted to collect data from a 2015 fully electric sedan equipped with a commercial adaptive cruise control system. Velocity, relative velocity, and space gap data collected during the experiments are used to calibrate two dynamical models for the ACC vehicle, one for each of two following settings. The models are calibrated via model-constrained optimization. The main finding is that the best fit models are unstable. To better understand how much the quality of the models would have to change to alter their stability, we calibrate the models with the constraint that they must be string stable and compare both the new model error as well as the calibrated parameter values. We find that the quality of fit for the minimum following setting degrades by 26%, while the quality of fit for the maximum following setting model only degrades by 7%, but requires significant changes in the parameter values.