Suppose a car is traveling at +24.8 m/s, and the driver sees a traffic light turn red. After 0.372 s has elapsed (the reaction time), the driver applies the brakes, and the car decelerates at 6.00 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, we first need to calculate the distance traveled during the driver's reaction time and the distance traveled while decelerating.
1. Calculate the distance traveled during the reaction time:
During the reaction time of 0.372 s, the car maintains a constant velocity of +24.8 m/s. The formula to calculate distance is given by:
distance = velocity * time
distance = 24.8 m/s * 0.372 s
distance = 9.2016 meters (rounded to four decimal places)
Therefore, the car traveled approximately 9.2016 meters during the reaction time.
2. Calculate the distance traveled while decelerating:
Using the kinematic equation:
v^2 = u^2 + 2as
where:
v = final velocity (0 m/s, as the car stops)
u = initial velocity (+24.8 m/s)
a = acceleration (-6.00 m/s^2, as it is decelerating)
s = distance
Rearranging the equation to solve for s, we get:
s = (v^2 - u^2) / (2a)
s = (0^2 - (24.8 m/s)^2) / (2 * -6.00 m/s^2)
s = -616.96 m^2/s^2 / -12.00 m/s^2
s = 51.4133 meters (rounded to four decimal places)
Therefore, the car traveled approximately 51.4133 meters while decelerating.
3. Calculate the total stopping distance:
The total stopping distance is the sum of the distances calculated in steps 1 and 2.
total stopping distance = distance during reaction time + distance while decelerating
total stopping distance = 9.2016 meters + 51.4133 meters
total stopping distance = 60.6149 meters (rounded to four decimal places)
Therefore, the total stopping distance of the car, as measured from the point where the driver first notices the red light, is approximately 60.6149 meters.