Final answer:
The total stopping distance for air brakes is longer primarily due to brake lag, as well as factors such as reaction time and effective braking. The calculation of total stopping distance includes the distance covered during the driver's reaction time plus the braking distance.
Step-by-step explanation:
The total stopping distance for a vehicle with air brakes compared to one with hydraulic brakes is longer primarily due to brake lag. This refers to the delay between the driver applying the brakes and the brakes actually engaging, which is typically greater in air brake systems. Additionally, reaction time plays a critical role in stopping distance. It involves the time it takes for a driver to recognize a need to stop and actually start the braking process. For example, if a car is traveling at 30.0 m/s and the driver has a reaction time of 0.500 s, the car will travel an additional 15.0 m during this reaction time before the brakes even begin to engage. The effective braking, which is the actual slowing down of the vehicle once the brakes are engaged, also affects the stopping distance. Wet or dry road conditions significantly influence the effective braking distance, with wetter conditions leading to longer stopping distances.
To calculate the total stopping distance, we consider the distance covered during the driver's reaction time and add it to the distance traveled during the actual braking process. This can be represented as: Xbraking + reaction = total. Understanding these concepts is important for driving safety and designing vehicle braking systems.