Final answer:
The total stopping distance needed to bring a car traveling at 20 m/s to rest, considering a driver's reaction time of 0.8 seconds and a deceleration rate of 20 m/s², is 26 meters. This value includes both the distance covered during the reaction time and the braking distance. The multiple-choice options provided in the question do not include the correct answer.
Step-by-step explanation:
The student has tasked us with calculating the total stopping distance of a car traveling at 20 m/s, taking into account the driver's reaction time and the deceleration due to braking. The driver's reaction time is given as 0.8 seconds, during which the car continues to move at 20 m/s before the brakes are applied. Once the brakes are applied, the car decelerates at a rate of 20 m/s² until it comes to rest.
To find the distance covered during the reaction time, we use the equation:
distance = speed × time. So we have:
- distance = 20 m/s × 0.8 s = 16 m
Next, we calculate the braking distance using the formula for deceleration:
distance = (final speed² - initial speed²) / (2 × deceleration), which simplifies to:
- distance = (0 - 20²) / (2 × -20) = 400 / 40 = 10 m
Adding the distance traveled during the reaction time to the braking distance gives us the total distance needed to bring the car to rest:
- total stopping distance = reaction distance + braking distance = 16 m + 10 m = 26 m
Since the correct option must have been wrongly omitted in the question's choices, we provide the correct total stopping distance, 26 m, which is not listed as one of the options of (a) 80 m, (b) 160 m, (c) 320 m, or (d) 640 m.