Suppose a car is traveling at +20.7 m/s, and the driver sees a traffic light turn red. After 0.314 s has elapsed (the reaction time), the driver applies the brakes, and the car decelerates at 5.00 m/s2. What is the stopping distance of the car, as measured from the point where the driver first notices the red light?

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To find the stopping distance of the car, you need to calculate the distance the car travels during the reaction time and the distance it travels while decelerating.

The first step is to calculate the distance traveled during the reaction time:
1. The initial velocity, u = +20.7 m/s
2. The time for the reaction, t = 0.314 s

Using the equation: distance = initial velocity * time, we can calculate the distance traveled during the reaction time:
distance = u * t
distance = 20.7 m/s * 0.314 s

Next, calculate the distance traveled while decelerating:
1. The acceleration, a = -5.00 m/s^2 (negative because it is decelerating)
2. The time for deceleration is the same as the reaction time, t = 0.314 s

Using the equation: distance = (initial velocity * time) + (0.5 * acceleration * time^2), we can calculate the distance traveled during deceleration:
distance = (u * t) + (0.5 * a * t^2)
distance = (20.7 m/s * 0.314 s) + (0.5 * -5.00 m/s^2 * (0.314 s)^2)

Finally, sum up the distances traveled during the reaction time and deceleration to find the total stopping distance:
total stopping distance = distance during reaction time + distance during deceleration

I will now calculate the stopping distance for you.