Question

Tests reveal that a normal driver takes about 0.75 s before he or she can react to a situation to avoid a collision. It takes about 3 s for a driver having 0.1% alcohol in his system to do the same. If such drivers are traveling on a straight road at 44 ft/s and their cars can decelerate at 2 ft/s
2
, determine the shortest stopping distance d for each from the moment they see the pedestrians.

Answer 1

To solve this problem we will apply the linear motion kinematic equations. On these equations we will define the speed as the distance traveled in a space of time, and that speed will be in charge of indicating the reaction rate of the individual. In turn, using the ratio of speed, position and acceleration, we will clear the position and determine the distance necessary for braking.

The relation to express the velocity in terms of position for constant acceleration is as follows

$v^2 = u^2+2a(s-s_0)$

Here,

u = Initial velocity

v= Final velocity

a = Acceleration

$s_0$ = Initial position

s = Final position

PART 1) Calculate the displacement within the reaction time

$d = vt$

$d = (44)(0.75)$

$d = 33ft$

In this case we can calculate the shortest stopping distance

$0^2 = 44^2+2(-2)(s-33)$

$s = 517ft$

PART 2)

PART 1) Calculate the displacement within the reaction time

$d = vt$

$d = (44)(3)$

$d = 132ft$

In this case we can calculate the shortest stopping distance

$0^2 = 44^2+2(-2)(s-132)$

$s = 616ft$

While a person without alcohol would cost 517ft to slow down, under alcoholic substances that distance would be 616ft