Respuesta :
Answer:
Extra distance traveled is 12.6 m
Explanation:
Initial constant speed of the car is given as
[tex]v = 95 km/h[/tex]
so it is given as
[tex]v = 95 \times \frac{1000 m}{3600 s}= 26.4 m/s[/tex]
now we know that the reaction time is 0.39 s when driver is unimpaired
so distance covered is given as
[tex]d_1 = 26.4 \times 0.39 = 10.3 m[/tex]
when driver is drunk then reaction time is 0.87 so the distance covered is given as
[tex]d_2 = 26.4 \times 0.87 = 23 m[/tex]
so the extra distance traveled by the person when he is drunk is given as
[tex]d = d_2 - d_1[/tex]
[tex]d = 23 - 10.3[/tex]
[tex]d = 12.6 m[/tex]
We can define speed as the quotient between the total distance traveled and the time it takes to travel that distance:
speed = distance/time
We can rewrite the above relation to:
distance = speed*time
With this, we will find that the drunk driver will travel 12.67 meters more than the sober driver.
The given information is:
The response time of a sober driver is:
t₁ = 0.39s
The response time of a drunk driver is:
t₂ = 0.87s
From this, if a car is initially traveling at 95km/h, the distance traveled by the car before the brakes are applied will be equal to the speed times the response time for each case.
Only note that the times are in seconds and the speed in hours, so we can rewrite the speed to meters over second, using:
1km = 1000m
1h = 3600s
Then:
[tex]95km/h = 95*(1000m/3600s) = 26.39 m/s[/tex]
Now we can get:
The distance for the sober driver will be:
[tex]d_1 = ( 26.39 m/s)*0.39s = 10.29m[/tex]
The distance for the drunk driver will be:
[tex]d_2 = (26.39 m/s)*0.87s = 22.96m[/tex]
The difference between these distances is:
[tex]d_2 - d_1 = 22.96m - 10.29m = 12.67m[/tex]
This means that the drunk driver will travel 12.67 meters more than the sober driver.
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