Driving is a common task that involves skill and individual preferences that can differ between drivers. The unique driving behaviours can be beneficial for differentiating drivers of shared vehicles and identifying differences between older drivers with normal and declining driving abilities. This paper presents a method for identifying individual drivers based on motor vehicle acceleration and deceleration events from their natural driving behaviour. We provide a novel approach to driver identification based on classification using multiple in-vehicle sensor signals collected in naturalistic conditions with anonymized driving locations. The dataset consists of thousands of trips from a selection of 14 stable-health older drivers (70 years and older) from their first year of the Candrive research study. We trained separate multiclass linear discriminant analysis classifiers to recognize unique patterns in their acceleration and deceleration events to predict the identity of the driver out of a group of drivers. For five different drivers, the acceleration and deceleration events were used to distinguish between drivers at 34% and 30% average accuracy, respectively. By taking a majority vote among the events, the accuracy improved to 61%, exceeding by about three times the null model of random guessing. This performance improvement continues when expanding the group from 2 to 14 drivers. The analysis shows potential for identifying drivers by the patterns in their driving maneuvers such as turning and stopping.