Final answer:
The total stopping distance for a car traveling at 15.8 m/s, after a reaction time of 0.882 s and braking at 6.10 m/s², is approximately 34.55 m.
Step-by-step explanation:
Stopping Distance Calculation
The stopping distance of a car involves two stages: the distance traveled during the driver's reaction time and the distance taken to stop the car after the brakes are applied (braking distance).
The total stopping distance is the sum of these two stages. In this scenario, the car is initially traveling at 15.8 m/s, and the driver has a reaction time of 0.882 s before applying the brakes, which results in a deceleration of 6.10 m/s².
Distance Traveled During Reaction Time
The car continues to travel at a constant speed during the driver's reaction time, so the distance covered in this time (d_reaction) is calculated using the formula:
d_reaction = speed × reaction time
d_reaction = 15.8 m/s × 0.882 s
= 13.936 m
Braking Distance
After the reaction time, the brakes are applied, and the car decelerates until it stops. We can calculate the braking distance (d_braking) using the kinematic equation:
v² = u² + 2as
where 'v' is the final velocity (0 m/s since the car stops), 'u' is the initial velocity (15.8 m/s), 'a' is the deceleration (-6.10 m/s²), and 's' is the stopping distance we want to find.
0 = (15.8 m/s)² + 2 × (-6.10 m/s²) × s
s = (15.8 m/s)² / (2 × 6.10 m/s²)
s = 20.61 m
Total Stopping Distance
The total stopping distance (d_total) is simply the sum of the distance during the reaction time and the braking distance:
d_total = d_reaction + d_braking
d_total = 13.936 m + 20.61 m
= 34.546 m (approx. 34.55 m)