Final answer:
Total stopping distance combines the reaction distance with the braking distance and will be longer on wet or icy roads due to reduced traction. It is not affected by the speed of the vehicle ahead or the type of car being driven. To calculate it, add the distance traveled during reaction time to the braking distance for specific road conditions.
Step-by-step explanation:
Total Stopping Distance in Vehicles
The total stopping distance of a vehicle is the sum of the reaction distance and the braking distance. The reaction distance is the length the vehicle travels during the driver's reaction time, which is before the brakes are applied. The braking distance is the length the vehicle travels after the brakes are applied until it comes to a complete stop. If you are driving on wet or icy roads, the total stopping distance will be greater due to reduced tire traction, increasing the braking distance.
If the road surface is smooth and dry, the total stopping distance tends to be shorter as there is better tire traction. The total stopping distance is not directly affected by the speed of the vehicle in front of you or whether you are driving a compact car. These factors may influence your driving behavior, but they do not change the physics of your car's stopping capability.
To calculate the total stopping distance, we can use the example of a car initially traveling at 30.0 m/s with a reaction time of 0.500 s. The distance traveled during the reaction time is calculated first, using a constant velocity, because there is no acceleration during this period (areaction = 0). For instance, if the car travels 15.0 m while the driver reacts (v = 30.0 m/s, treaction = 0.500 s), you would then add this distance to the braking distance determined for either dry or wet conditions to get the total displacement.