Final answer:
The total stopping distance for vehicles with air brakes is greater than hydraulic brakes primarily due to the longer reaction distance required to engage the brakes.
Step-by-step explanation:
The total stopping distance for vehicles with air brakes is longer than that for vehicles with hydraulic brakes due to reaction distance. The total stopping distance is composed of the reaction distance, which is the distance covered from the moment a driver perceives a signal to apply brakes (like a light turning red) and the actual moment when the brakes are applied, as well as the braking distance, which is the distance it takes for the vehicle to come to a complete stop after the brakes are applied.
In the context of vehicles, when comparing air brakes to hydraulic brakes, the response time for the braking system to engage could be longer for air brakes, hence, prolonging the reaction distance.
It is vital to understand that the total stopping distance will vary depending on road conditions, vehicle speed, and reaction time. According to the information provided, assuming a 0.500 second reaction time, a car traveling at 30.0 m/s will travel a certain distance before actual deceleration begins.