The speed limit in a school zone is 40 km/h. A driver traveling at this speed sees a child run into the road 23 m ahead of hs car. He applies the brakes, and the car decelerates at a uniform rate of 8.0m/s^2. if the driver's reaction time is .25s, will the car stop before hitting the child?
basically is 69+9999=10068 and then u find 3% of 10068 which is 302.04 and then u find 3/4 of 302.04=226.53 and then u add 9 to it which is 235.53 and u divide that by 69 which is 3.413 thats ur answer
Using Vf = Vi + at we can calculate how long it will take the car to stop from 11.11 m/s. It will take 1.39s but the reaction time adds .25s so it the time it takes will be 1.64s to stop the car.
Now use S = Vit + (1/2)at^2 to see if the car will stop before 23m.
To determine if the car will stop before hitting the child, we need to calculate the distance it will take for the car to come to a stop after the driver applies the brakes.
Given:
Initial speed (v0) = 40 km/h = (40 * 1000) m / (3600 s) = 11.11 m/s
Deceleration (a) = -8.0 m/s^2 (negative because it is decelerating)
Reaction time (t) = 0.25 s
Distance between car and child (s) = 23 m
The total distance covered by the car during the reaction time is:
distance_reaction = v0 * t = 11.11 m/s * 0.25 s = 2.78 m
Next, we need to calculate the distance covered by the car while decelerating:
distance_deceleration = (0 - v1^2) / (2a), where v1 is the final velocity when the car stops.
Using the formula v = u + at, where u is the initial velocity, a is the acceleration, and t is the time, we can find v1:
0 = 11.11 m/s + (-8.0 m/s^2) * t
t = 11.11 m/s / (8.0 m/s^2) = 1.39 s
Now, we can calculate the distance covered while decelerating:
distance_deceleration = (0 - (11.11 m/s + (-8.0 m/s^2) * 1.39 s)^2) / (2 * -8.0 m/s^2)
Plugging in the values:
distance_deceleration = (0 - (11.11 m/s - 11.12 m/s)^2) / (-16.0 m/s^2)
= (0 - (-0.01 m/s)^2) / (-16.0 m/s^2)
= -0.01 m^2/s^2 / (-16.0 m/s^2)
= 0.01 m^2 / (16.0 s^2)
= 0.0006 m
Finally, to calculate the total stopping distance, we add the distance covered during the reaction time to the distance covered while decelerating:
total_stopping_distance = distance_reaction + distance_deceleration
= 2.78 m + 0.0006 m
= 2.78 m
Since the total stopping distance is 2.78 m and the distance between the car and the child is 23 m, the car will not stop before hitting the child.
To determine whether the car will stop before hitting the child, we need to calculate the stopping distance of the car and compare it to the distance between the car and the child initially.
First, let's calculate the stopping distance. To do this, we need to find two components: the distance traveled during the driver's reaction time and the distance traveled while decelerating.
1. Distance traveled during the driver's reaction time:
During the reaction time of 0.25 seconds, the car continues to move at the initial speed. We can calculate this distance using the formula:
Distance = Initial speed × Reaction time
Distance = 40 km/h × 0.25 s
Let's convert the initial speed from km/h to m/s:
Initial speed = 40 km/h = (40 × 1000) m/ (60 × 60) s = 11.11 m/s
Now we can calculate the distance traveled during the reaction time:
Distance = 11.11 m/s × 0.25 s
2. Distance traveled while decelerating:
The car decelerates at a uniform rate of 8.0 m/s^2. We need to calculate the distance traveled during the deceleration phase using the formula:
Distance = (Initial speed)^2 / (2 × Acceleration)
Distance = (11.11 m/s)^2 / (2 × 8.0 m/s^2)
Now let's calculate both distances and add them together:
Distance = Distance during reaction time + Distance during deceleration
If the total distance is greater than the initial distance between the car and the child (23 m), then the car will stop before hitting the child.
Now, I will calculate the distances and check if the car stops before hitting the child.