Suppose a car is traveling at +15.0 m/s, and the driver sees a traffic light turn red. After 0.405 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
during 0.405 sec there is no acceleration;
therefore,
V=d/t
d=vt
d=(15)(0.405)
which is the distance car traveled before driver hits brake.
Now, a=-6 m/s^2 and car's final velocity vf=0. initial velocity vo=15 m/s
use
vf^2 = vo^2 +2as
to get s=distance traveled under acceleration.
s+d is your answer.
To find the stopping distance of the car, we can use the equations of motion.
1. The initial velocity (u) is +15.0 m/s.
2. The acceleration (a) is -6.00 m/s^2 (negative because it is deceleration).
3. The time (t) is 0.405 s.
4. The final velocity (v) is 0 m/s (the car comes to a stop).
We can use the equation of motion: v = u + at to find the final velocity:
0 = 15.0 + (-6.00)t
Simplifying the equation:
-6.00t = -15.0
t = -15.0 / -6.00
t = 2.50 s
The car takes 2.50 s to come to a stop.
Now, we can calculate the stopping distance using the equation of motion: s = ut + (1/2)at^2
s = (15.0)(0.405) + (1/2)(-6.00)(0.405)^2
s = 6.075 - 0.492
s = 5.583 m
Therefore, the stopping distance of the car, as measured from the point where the driver first notices the red light, is 5.583 meters.
To find the stopping distance of the car, we need to calculate the distance traveled during the driver's reaction time and the distance traveled during the deceleration.
1. Calculate the distance traveled during the driver's reaction time:
During the reaction time, the car maintains a constant speed of +15.0 m/s. The distance traveled is given by:
Distance = Speed x Time
Distance = 15.0 m/s x 0.405 s
Distance = 6.075 m
2. Calculate the distance traveled during deceleration:
Using the equation of motion:
v² = u² + 2as
where:
v = final velocity (0 m/s as the car comes to a stop)
u = initial velocity (+15.0 m/s)
a = acceleration (-6.00 m/s²)
s = distance
Rearranging this equation to solve for distance, we have:
s = (v² - u²) / (2a)
Plugging in the values:
s = (0 m/s)² - (+15.0 m/s)² / (2 x -6.00 m/s²)
s = -225.0 m²/s² / -12.00 m/s²
s = 18.750 m
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 during deceleration:
Total Stopping Distance = Distance during Reaction Time + Distance during Deceleration
Total Stopping Distance = 6.075 m + 18.750 m
Total Stopping Distance = 24.825 m
Therefore, the stopping distance of the car, as measured from the point where the driver first notices the red light, is 24.825 meters.