Suppose a car is traveling at +22.3 m/s, and the driver sees a traffic light turn red. After 0.351 s has elapsed (the reaction time), the driver applies the brakes, and the car decelerates at 8.00 m/s2. What is the stopping distance of the car, as measured from the point where the driver first notices the red light?
stopping distance:
22.3*.351 + braking
but braking can be found from
vf^2=vi^2+2ad solve for d. vf=0, a given, vi=22.3
add the distances.
To find the stopping distance of the car, we need to calculate the distance traveled during the reaction time and the distance traveled while decelerating.
1. Distance traveled during the reaction time:
The car is traveling at a constant speed during the reaction time. The formula to calculate the distance traveled at a constant speed is:
Distance = Speed x Time
Given that the car is traveling at +22.3 m/s and the reaction time is 0.351 s, we can substitute these values into the formula:
Distance_travelled_reaction_time = 22.3 m/s x 0.351 s
Calculating the reaction time distance gives us:
Distance_travelled_reaction_time = 7.8093 m
2. Distance traveled while decelerating:
To calculate the distance traveled while decelerating, we can use the following kinematic equation:
Distance = (Initial Velocity^2 - Final Velocity^2) / (2 * Acceleration)
Given that the initial velocity of the car is +22.3 m/s, the final velocity is 0 m/s (since the car needs to stop), and the acceleration is -8.00 m/s^2 (negative value because it represents deceleration), we can substitute these values into the formula:
Distance_travelled_deceleration = (22.3^2 - 0^2) / (2 * -8.00)
Calculating the deceleration distance gives us:
Distance_travelled_deceleration = 62.6625 m
3. Total stopping distance:
To find the total stopping distance, we add the distance traveled during the reaction time to the distance traveled while decelerating:
Total_stopping_distance = Distance_travelled_reaction_time + Distance_travelled_deceleration
Substituting the calculated values:
Total_stopping_distance = 7.8093 m + 62.6625 m
Calculating the total stopping distance gives us:
Total_stopping_distance = 70.4718 m
Therefore, the stopping distance of the car, as measured from the point where the driver first notices the red light, is approximately 70.4718 meters.