Answer to Question #155181 in Civil and Environmental Engineering for Shin

Question

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.

Answer 1

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.