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Alcohol consumption slows people's reaction times. In a controlled government test, it takes a certain driver t 1 = 0.27 s to hit the brakes in a crisis when unimpaired and t 2 = 1.09 s when drunk. If the car is initially traveling at v = 91 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?

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Answer:

20.7278 m

Explanation:

Reaction time [tex]t_1=0.27\ s[/tex]

Distance traveled in the reaction time

[tex]s=vt\\\Rightarrow s=\dfrac{91}{3.6}\times 0.27=6.825\ m[/tex]

Reaction time [tex]t_2=1.09\ s[/tex]

Distance traveled in the reaction time

[tex]s=vt\\\Rightarrow s=\dfrac{91}{3.6}\times 1.09[/tex]

If at both times the deceleration is the same then the difference in distance is

[tex]\dfrac{91}{3.6}\times 1.09-6.825=20.7278\ m[/tex]

The distance traveled farther is 20.7278 m