Suppose a car is traveling at +23.7 m/s, and the driver sees a traffic light turn red. After 0.427 s has elapsed (the reaction time), the driver applies the brakes, and the car decelerates at 9.00 m/s2. What is the stopping distance of the car, as measured from the point where the driver first notices the red light?
For the reaction time,
distance = velocity * time
= 23.7*0.427
= 10.12 m
For the braking time,
v²-u^sup2;=2aS
v=0, u=23.7 m/s, a=-9 m/s^2,
S=(v²-u^sup2;)/(2a)
=-23.7^sup2/(2*(-9))
=32.21 m
Stopping distance is the sum of the two distances.
To calculate the stopping distance of the car, we need to determine the time the car takes to come to a complete stop, and then use that time to calculate the distance traveled during deceleration.
First, let's find the time it takes for the car to stop after the driver applies the brakes. We know that the initial velocity (v0) is +23.7 m/s, and the deceleration (a) is -9.00 m/s^2 (negative because it is in the opposite direction of motion).
We can use the equation of motion:
v = v0 + at
Where:
- v is the final velocity (which is 0 because the car comes to a stop),
- v0 is the initial velocity,
- a is the acceleration/deceleration, and
- t is the time.
Rearranging the equation, we get:
t = (v - v0) / a
Substituting the given values into the equation, we get:
t = (0 - 23.7) / (-9.00) = 2.63333 s
Now that we have the time it takes for the car to stop, we can calculate the stopping distance using the equation of motion:
s = v0 * t + (1/2) * a * t^2
Substituting the values, we get:
s = 23.7 * 2.63333 + (1/2) * (-9.00) * (2.63333)^2
Evaluating the equation, we find:
s = 31.2847 - 19.8018 = 11.4829 m
Therefore, the stopping distance of the car, as measured from the point where the driver first notices the red light, is approximately 11.5 meters.