Like all man-made artifacts, Advanced Driver Assistance Systems have certain limitations beyond which they cannot function properly or work at all. The users in the driving domain have diverse backgrounds and it is likely that many of them start interacting with the technology without having gained detailed knowledge, such as by reading user manuals. This study explores whether drivers with only minimal knowledge of the Lane Departure Warning system can recognize the system's speed threshold and update themselves about this in a dynamic driving environment. Since drivers are not always single-mindedly focused on driving so participants were divided into two groups. Group 1 subjects performed only the driving task, while Group 2 was prompted to carry out a secondary task in addition to the primary driving task. Our investigation allowed us to estimate the effects of drivers' minimal mental model of the system working due to lack of sufficient knowledge concerning its capacities upon their 1) learning from experience and 2) situation awareness. It was assumed that the demands of multitasking would impair the driver's ability to observe the system's state and delay the mental model improvement process, compared to a setting in which driving was the only task. Experiment results using a driving simulator have been presented. The results revealed that the number of the drivers, who did not become aware of the operating condition of the LDW system, was quite high for both groups regardless of the nature of their tasks. It had been deduced that the users' preconceptions and expectations due to their limited knowledge about the capacities of the technology, could make them rely on the system to alert them in different situations even when the system was not operating. Hence, these factors can not only adversely affect the social benefits associated with ADAS, but also the acceptance and usability of these systems.