Suppose a car is traveling at +23.8 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 7.00 m/s2. What is the stopping distance of the car, as measured from the point where the driver first notices the red light?

62m

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.

First, let's find the distance traveled during the reaction time using the formula:
distance = initial velocity * time + 0.5 * acceleration * time^2

Given:
initial velocity (v0) = +23.8 m/s (since it is positive, we take it as the magnitude)
time (t) = 0.351 s
acceleration (a) = 0 m/s^2 (since there is no acceleration during the reaction time)

Calculating the distance traveled during the reaction time:
distance_reaction = v0 * t + 0.5 * a * t^2
= 23.8 * 0.351 + 0.5 * 0 * 0.351^2
= 8.347 m

Now, let's calculate the distance traveled while decelerating using the formula:
distance = (final velocity^2 - initial velocity^2) / (2 * acceleration)

Given:
initial velocity (v0) = +23.8 m/s (since it is positive, we take it as the magnitude)
final velocity (vf) = 0 m/s (since the car stops)
acceleration (a) = -7.00 m/s^2 (opposite direction of motion, so it is negative)

Calculating the distance traveled while decelerating:
distance_deceleration = (vf^2 - v0^2) / (2 * a)
= (0^2 - 23.8^2) / (2 * -7.00)
= -566.44 m

Note: The negative value indicates that the distance is in the opposite direction of the initial motion.

Finally, the stopping distance of the car is the sum of the distance traveled during the reaction time and the distance traveled while decelerating:
stopping distance = distance_reaction + distance_deceleration
= 8.347 + (-566.44)
= -558.093 m

So, the stopping distance of the car, as measured from the point where the driver first notices the red light, is approximately 558.093 meters in the opposite direction of the initial motion.