Laboratory studies of abstract, highly controlled tasks point towards noisy evidence accumulation as a key mechanism governing decision making. Yet it is unclear whether the cognitive processes implicated in simple, isolated decisions in the lab are as paramount to decisions that are ingrained in more complex behaviors, such as driving. Here we aim to address the gap between modern cognitive models of decision making and studies of naturalistic decision making in drivers, which so far have provided only limited insight into the underlying cognitive processes. We investigate drivers' decision making during unprotected left turns, and model the cognitive process driving these decisions. Our model builds on the classical drift-diffusion model, and emphasizes, first, the drift rate linked to the relevant perceptual quantities dynamically sampled from the environment, and, second, collapsing decision boundaries reflecting the dynamic constraints imposed on the decision maker’s response by the environment. We show that the model explains the observed decision outcomes and response times, as well as substantial individual differences in those. Through cross-validation, we demonstrate that the model not only explains the data, but also generalizes to out-of-sample conditions, effectively providing a way to predict human drivers’ behavior in real time. Our results reveal the cognitive mechanisms of gap acceptance decisions in human drivers, and exemplify how simple cognitive process models can help us to understand human behavior in complex real-world tasks.