Suppose a car is traveling at +25.0 m/s, and the driver sees a traffic light turn red. After 0.564 s has elapsed (the reaction time), the driver applies the brakes, and the car decelerates at 4.00 m/s2. What is the stopping distance of the car, as measured from the point where the driver first notices the red light?

d = Vo*t + (-Vo^2/2a) = 25*0.564 + -(25^2)/-8 = 92.2 m.

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. Calculate the distance traveled during the reaction time:
Given:
Initial velocity, u = +25.0 m/s
Time, t = 0.564 s

Using the equation:
Distance = Initial velocity * Time

Distance during reaction time = 25.0 m/s * 0.564 s = 14.10 m

2. Calculate the distance traveled while decelerating:
Given:
Acceleration, a = -4.00 m/s²
Time, t = ?

Using the equation:
Final velocity² = Initial velocity² + 2 * acceleration * distance

We need to find the time taken to come to a stop, so the final velocity will be 0 m/s.

0 m/s = (25.0 m/s)² + 2 * (-4.00 m/s²) * distance

Simplifying the equation:
0 = 625.0 m²/s² - 8.00 m/s² * distance

Rearranging the equation:
8.00 m/s² * distance = 625.0 m²/s²

distance = 625.0 m²/s² / 8.00 m/s²
distance = 78.1 m

3. Calculate the total stopping distance:
Total stopping distance = Distance during reaction time + Distance traveled while decelerating
Total stopping distance = 14.10 m + 78.1 m
Total stopping distance = 92.2 m

Therefore, the stopping distance of the car, as measured from the point where the driver first notices the red light, is 92.2 meters.

To calculate the stopping distance of the car, we need to consider two components: the distance covered during the driver's reaction time and the distance covered while decelerating.

1. Distance covered during the reaction time:
During the reaction time of 0.564 s, the car continues to move forward at a constant velocity of +25.0 m/s (since no force is acting to decelerate it).
The formula to calculate the distance covered during this time is:
Distance = Velocity x Time
Distance = 25.0 m/s x 0.564 s
Distance = 14.1 meters

2. Distance covered while decelerating:
To calculate the distance covered while decelerating, we need to use the kinematic equation:
vf^2 = vi^2 + 2ad

Where:
vf = final velocity (0 m/s as the car comes to a stop)
vi = initial velocity (+25.0 m/s)
a = acceleration (-4.00 m/s^2)
d = distance

Rearranging the equation to solve for distance (d):
d = (vf^2 - vi^2) / (2a)

Substituting the values:
d = (0^2 - (25.0)^2) / (2*(-4.00))
d = -625 / (-8)
d = 78.125 meters (rounded to three decimal places)

Therefore, the stopping distance of the car, as measured from the point where the driver first notices the red light, is the sum of the distance covered during the reaction time and the distance covered while decelerating:
Stopping distance = 14.1 meters + 78.125 meters
Stopping distance = 92.225 meters (rounded to three decimal places)