Alert driver vs Sleepy Driver distance traveled

In summary, the sleepy driver will take an additional 10 car lengths to stop compared to the alert driver due to their slower reaction time. This can be calculated by finding the total distance traveled by each driver and then subtracting the distance traveled by the alert driver from the distance traveled by the sleepy driver, and dividing the resulting difference by the typical car length of 5.0 m.
  • #1
smsport
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A car is traveling at 120 km/h (75 mph). When applied the braking system can stop the car with a deceleration rate of 9.0 m/s2. The typical reaction time for an alert driver is 0.50 s versus 2.0 s for a sleepy driver. Assuming a typical car length of 5.0 m, calculate the number of additional car lengths it takes the sleepy driver to stop compared to the alert driver.

I worked this out first by using v^2=Vo^2 + 2a(Δx) to get the distance traveled
0= 33.3m/s^2 + (-9m/s^2)(x)
x= 61.7m

Then, I used d= vt for driver #1: (33.3m/s)(.5s)= 16.7m
and for driver #2: (33.3m/s)(2.0s)= 66.7m

Then, I added 61.7m to each driver's distance:
driver #1 total dist traveled=78.4m
driver #2 total dist traveled= 128.4m

Then, subtract 78.4m from 128.4m to get the total extra distance traveled by the sleepy driver. Then, divide this figure by 5m to get total car lengths additional.

128.4m- 78.4m = 50m/5m= 10 car lengths.

Now, after going through the problem it appears my initial step is really unnecessary because I could have just used d=vt for driver #1 and driver #2 and took the difference of those figures divided by 5m to get car lengths extra for the sleepy driver. Am I correct? Unless the question was asking for total distance traveled by both or either driver, then step #1 isn't even needed and this problem could have solved much quicker.

Please confirm.

Thanks!
 
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  • #2
Yes

d1=vt1 +(v2/2a)

d2=vt2 +(v2/2a)

Δd=d2-d1
 
Last edited:

What is the difference in distance traveled between an alert driver and a sleepy driver?

The distance traveled by an alert driver and a sleepy driver can vary greatly depending on the circumstances. However, research has shown that an alert driver can cover a significantly longer distance compared to a sleepy driver.

Why do alert drivers travel a longer distance compared to sleepy drivers?

An alert driver is able to maintain a steady speed and make fewer errors while driving. They are also able to react quickly to unexpected situations on the road. In contrast, a sleepy driver may have slower reaction times and may make more mistakes, resulting in a shorter distance traveled.

What factors can affect the distance traveled by an alert driver?

The distance traveled by an alert driver can be affected by various factors such as road conditions, traffic, weather, and the driver's level of experience and skill. Additionally, the type of vehicle and its condition can also play a role in the distance traveled.

How does fatigue impact the distance traveled by a driver?

Fatigue can significantly affect a driver's ability to travel long distances. It can lead to drowsiness, decreased reaction times, and impaired decision-making, all of which can result in a shorter distance traveled. It is important for drivers to take breaks and rest when feeling fatigued in order to maintain safe driving practices.

Can technology help to increase the distance traveled by a driver?

Yes, certain technologies such as lane departure warning systems, automatic emergency braking, and adaptive cruise control can help drivers to maintain their alertness and decrease the likelihood of accidents, ultimately allowing them to cover a longer distance safely.

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