A car is traveling at 16.0 m/s, and the driver sees a traffic light turn red. After 0.500 s (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 sees the red light?

.5 * 16 = 8 meters before brakes so add that at the end

v = Vi - 8 t
0 = 16 - 8 t at stop
t = 2 seconds braking

d = Vi t - (1/2) a t^2
d = 16*2 - 4 (4)
d = 16 meters

8 + 16 = 24 meters

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.

Step 1: Calculate the distance traveled during the reaction time.
The formula for distance traveled during a constant speed is given by:
Distance = Speed × Time

The car is traveling at a constant speed of 16.0 m/s for a reaction time of 0.500 s. Therefore, the distance traveled during the reaction time is:
Distance = 16.0 m/s × 0.500 s = 8.00 m

Step 2: Calculate the distance traveled while decelerating.
To find the distance traveled while decelerating, we can use the following formula:
Distance = (Initial Velocity^2 - Final Velocity^2) / (2 × Acceleration)

Here, the initial velocity is 16.0 m/s, the final velocity is 0 m/s (since the car stops), and the acceleration is -8.00 m/s^2 (negative due to deceleration).
Therefore, the distance traveled while decelerating is:
Distance = (16.0 m/s)^2 - (0 m/s)^2 / (2 × -8.00 m/s^2)
Distance = 256 m^2/s^2 / -16 m/s^2
Distance = -16 m

Since distance cannot be negative, we take the absolute value:
Distance = 16 m

Step 3: Calculate the total stopping distance.
The total stopping distance is the sum of the distance traveled during the reaction time and the distance traveled while decelerating:
Total Stopping Distance = Distance during Reaction Time + Distance while Decelerating
Total Stopping Distance = 8.00 m + 16 m
Total Stopping Distance = 24.0 m

Therefore, the stopping distance of the car, as measured from the point where the driver first sees the red light, is 24.0 meters.

To find the stopping distance of the car, we need to analyze the motion of the car during the reaction time and the time it takes to decelerate to a stop.

First, let's calculate the distance the car travels during the reaction time. The formula to find the distance traveled with constant velocity is:

Distance = Velocity * Time

In this case, the velocity during the reaction time is 16.0 m/s, and the reaction time is 0.500 s. Therefore:

Distance = 16.0 m/s * 0.500 s
Distance = 8.00 meters

During the reaction time, the car will travel 8.00 meters.

Next, let's calculate the stopping distance while the car decelerates. We can use the following equation of motion:

vf^2 = vi^2 + 2 * a * d

Where:
- vf is the final velocity (which is 0 because the car comes to a stop)
- vi is the initial velocity (which is 16.0 m/s)
- a is the acceleration (which is -8.00 m/s^2, taking the negative sign because it's deceleration)
- d is the stopping distance we're trying to find

Rearranging the equation, we can solve for d:

d = (vf^2 - vi^2) / (2 * a)
d = (0^2 - 16.0^2) / (2 * -8.00)
d = (-256.0) / (-16.00)
d = 16.00 meters

Hence, the stopping distance of the car, as measured from the point where the driver first sees the red light, is 16.00 meters.