Question #155243

a test of a driver's perception reaction time is being conducted on a special testing track with wet pavement and a driving speed of 50 kph. when the driver is sober, a stop can be made just in time to avoid hitting an object that is visible 40 m. ahead. after a few drinks of san miguel beer, under exactly the same condition, the driver fails to stop in time and strikes the object at a speed of 30 kph. determine the driver's perception-reaction time after he was drinking. assume coefficient of friction is 0.60.

Expert's answer

"d= v"_{1 }"\\times tr"

"d=" distance travelled for perception

"v"_{1} = initial velocity

"tr"= perception time

"tr" ="\\frac{d}{v1}" = "\\frac{40}{50}= 0.8 seconds"

coefficient of friction "\\mu" = "\\frac{force applied }{normal weight }"= "\\frac{ma}{mg}"

0.6="\\frac{mg}{ma}= \\frac{ma}{m\\times 9.81}"

"a=9.81\\times0.6=5.886 m\/s"

"a" (acceleration/deceleration) = "\\frac{final velocity- initial velocity}{time^2}"

= "\\frac{mg}{t}" ="v"_{v}- "v"_{u/t}"2"

5.886= "\\frac{0-30}{t^2}=equivalent = \\frac{30}{t^2}"

t= "\\sqrt[]{\\frac{30}{5.886}} = 2.258 seconds"

total perception time for the unconscious driver is therefore prolonged as below;

t= 0.8 + 2.258

= 3.058 seconds

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