Final answer:
To calculate the stopping distance and time with a reaction time of 0.16 seconds, the distance traveled during reaction time and stopping distance under deceleration are added, resulting in approximately 28.982 meters, and the stopping time is approximately 3.426 seconds.
Step-by-step explanation:
The question relates to the concepts of reaction time, deceleration, and stopping distance in the context of Physics.
First, let's assess the given reaction time of 0.16 seconds. With the car moving at a constant speed of 35 mph, which is approximately 15.65 m/s (1 mile = 1,609.34 meters), we need to calculate the distance traveled during the reaction time before braking begins. This is calculated by multiplying the speed by the reaction time:
- Distance During Reaction Time (DRT) = speed × reaction time = 15.65 m/s × 0.16 s = 2.504 m.
Next, using the formula for stopping distance under constant deceleration:
- Stopping Distance (SD) = (speed²) / (2 × deceleration) = (15.65 m/s)² / (2 × 4.57 m/s²) = 26.478 m approximately.
To find the total stopping distance, add the reaction distance to the stopping distance, which would be 2.504 m + 26.478 m = 28.982 m.
As for the stopping time, since the deceleration is constant, we can use the formula:
- Stopping Time (ST) = speed / deceleration = 15.65 m/s / 4.57 m/s² = 3.426 s approximately.
While the question seems to ask for specific answers likely from an accompanying multiple-choice list, these calculations provide the rationale to correctly choose the closest options for stopping distance and stopping time.