Alcohol consumption slows people's reaction times. in a controlled government test, it takes a certain driver t1=0.39 s to hit the brakes in a crisis when unimpaired and t2=0.87 s when drunk. if the car is initially traveling at v=95 km/h, how much farther does the car travel before the brakes are applied when the person is drunk than it travels when the person is sober?

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:

Now we can get:

The distance for the sober driver will be:

The distance for the drunk driver will be:

The difference between these distances is:

This means that the drunk driver will travel 12.67 meters more than the sober driver.

If you want to learn more, you can read:

link

Extra distance traveled is 12.6 m

Explanation:

Initial constant speed of the car is given as

so it is given as

now we know that the reaction time is 0.39 s when driver is unimpaired

so distance covered is given as

when driver is drunk then reaction time is 0.87 so the distance covered is given as

so the extra distance traveled by the person when he is drunk is given as