Wrong , the time it takes to slide the foot from he gas pedal to the brake is insignificant in comparison to the "mental processing time" and the "physics involved in stopping the momentum of the vehicle".
Mechanical devices take time to engage, even after the responder has acted. For example, a driver stepping on the brake pedal does not stop the car immediately. Instead, the stopping is a function of physical forces, gravity and friction.
Here's a simple example. Suppose a person is driving a car at 55 mph (80.67 feet/sec) during the day on a dry, level road. He sees a pedestrian and applies the brakes. What is the shortest stopping distance that can reasonably be expected? Total stopping distance consists of three components:
- Reaction Distance. First. Suppose the reaction time is 1.5 seconds. This means that the car will travel 1.5 x80.67 or 120.9 feet before the brakes are even applied.
- Brake Engagement Distance. Most reaction time studies consider the response completed at the moment the foot touches the brake pedal. However, brakes do not engage instantaneously. There is an additional time required for the pedal to depress and for the brakes to engage. This is variable and difficult to summarize in a single number because it depends on urgency and braking style. In an emergency, a reasonable estimate is .3 second, adding another 24.2 feet.
- Physical Force Distance. Once the brakes engage, the stopping distance is determined by physical forces (D=S²/(30*f) where S is mph) as 134.4 feet.
Total Stopping Distance = 120.9 ft + 24.2 ft + 134.4 ft = 279.5 ft
Almost half the distance is created by driver reaction time. This is one reason that it is vital to have a good estimate of speed of human response.