# Stopping distance w human reaction time

• afa
In summary, the stopping distance for a car with an initial speed of 26.9 m/s and a human reaction time of 0.9s for an acceleration of -4m/s^2 is 114.66125 meters. This is calculated by adding the distance covered during the reaction time (24.21 meters) to the distance traveled during the deceleration time (90.45125 meters). It is important to double check these calculations as the expert providing this summary is not an AP physics student.
afa

## Homework Statement

determine the stopping distance for a car with an intitial speed of 26.9 m/s and a human reaction time of 0.9s for an acceleration of -4m/s^2

## Homework Equations

x=vt t=v/a x=x+vt+.5at^2

## The Attempt at a Solution

I used the second equation to find total time by adding it to .9s then plugged that into equation 3 and added that to x of the first equation?? what am i doing wrong??

Alright, you are going 26.9 m/s. When you stop, you take .9s before the deceleration takes place.

So, it's .9 seconds plus however much time the deceleration takes.

As such,
Alright, you are going 26.9 m/s. When you stop, you take .9s before the deceleration takes place.

So, it's .9 seconds plus however much time the deceleration takes.

As such,
(Original Velocity)/(Deceleration rate)=Total Deceleration Time
(26.9m/s)/(4m/s^2)=Total Deceleration Time
6.725 seconds= Total Deceleration Time

Stopping Distance=(Average Velocity)(Total Deceleration Time)
(.5)(26.9 m/s)(6.725 seconds)=90.45125 meters

Now, you know how much distance it takes to stop.
You have to add how much distance you covered before stopping.
(reaction time)(velocity during reaction time)=Distance traversed during reaction time
(.9 seconds)(26.9m/s)=24.21 meters

24.21 meters + 90.45125 meters= 114.66125 meters

thank you so much, you seem to be the most helpful, do you think you could help me out on some more?

Certainly. How else would I postpone doing my chemistry work? And I haven't actually taken AP physics, so I suggest checking my answers that I give you. I just like math and am good at figuring stuff out.

I would suggest that you first define your variables and units clearly in order to avoid confusion. In this case, the initial speed should be given in meters per second (m/s), the acceleration in meters per second squared (m/s^2), and the human reaction time in seconds (s). Additionally, you should specify what the final stopping distance is being measured in (meters, kilometers, etc.).

Once your variables and units are defined, you can use the equations of motion to solve for the stopping distance. The first equation, x=vt, can be used to find the distance traveled during the reaction time of 0.9 seconds. The second equation, t=v/a, can be used to find the total time it takes for the car to come to a complete stop. Finally, the third equation, x=x+vt+.5at^2, can be used to find the total stopping distance.

Therefore, your solution should look something like this:

Given:
Initial speed (v) = 26.9 m/s
Acceleration (a) = -4 m/s^2
Human reaction time (t) = 0.9 s

Using x=vt, the distance traveled during the reaction time is:
x = (26.9 m/s)(0.9 s) = 24.21 m

Using t=v/a, the total time it takes for the car to stop is:
t = (26.9 m/s)/(-4 m/s^2) = -6.725 s

Using x=x+vt+.5at^2, the total stopping distance is:
x = 24.21 m + (26.9 m/s)(-6.725 s) + 0.5(-4 m/s^2)(-6.725 s)^2
x = 24.21 m - 180.53 m + 90.265 m = -66.055 m

Therefore, the stopping distance for a car with an initial speed of 26.9 m/s and a human reaction time of 0.9 s for an acceleration of -4m/s^2 is approximately 66.055 meters.

It is important to note that this solution assumes ideal conditions and does not take into account factors such as road conditions, tire grip, and human error, which can affect the actual stopping distance

## 1. How is stopping distance affected by human reaction time?

Stopping distance is directly affected by human reaction time. This is the time it takes for a person to perceive a hazardous situation and react by applying the brakes. The longer the reaction time, the longer the stopping distance will be.

## 2. What is considered a normal human reaction time?

On average, human reaction time is around 0.25 seconds. However, this can vary depending on age, gender, and other factors. Some individuals may have a faster or slower reaction time than the average.

## 3. How does speed affect stopping distance with human reaction time?

The higher the speed, the longer the stopping distance will be. This is because the vehicle will cover a greater distance while the driver is reacting to a situation. It is important to maintain a safe speed to allow for enough reaction time and stopping distance.

## 4. Can human reaction time be improved?

Yes, with practice and training, human reaction time can be improved. Activities such as playing sports, video games, and driving simulations can help improve reaction time. Additionally, staying alert and avoiding distractions while driving can also help improve reaction time.

## 5. What factors can affect human reaction time?

There are several factors that can affect human reaction time, including age, fatigue, alcohol or drug use, distractions, and physical or mental impairments. It is important to be aware of these factors and take necessary precautions to maintain a safe reaction time while driving.

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