Question #155181

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

The driver's perception-reaction time is:

"t=t_1-t_2" ,

where "t_1" - the time from the moment, when the driver presses the brake, to the moment, when the car stops;

"t_2" - the time from the moment, when the driver presses the brake, to the moment, when the car strikes the object at a speed of 30 kmph.

First, find "t_1". The car speed depends on time as follows:

"v=v_0+at" ,

where "v_0" - the initial speed;

"a" - the acceleration.

In the first case "v=0", so

"t_1=-\\frac{v_0}{a}" .

The acceleration can be found from the Newton's second law:

"ma=-\\mu mg,"

"a=-\\mu g."

Henсe, assuming that 50 kmph is 13,89 mps,

"t_1=\\frac{v_0}{\\mu g}=\\frac{13.89}{0.6\\cdot 9.81}=2.36\\space s."

Then, find "t_2". In the second case "v=30\\space kmph" or "8.33\\space mps" so

"t_2=\\frac{v_0-v}{\\mu g}=\\frac{13.89-8.33}{0.6\\cdot 9.81}=0.95\\space s."

"t=t_1-t_2=2.36-0.95=1.41\\space s."

Answer: The driver's perception-reaction time is 1.41 seconds.

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