Your car\'s stopping distance , according to a chart in the Alabama Driver\'s Ma

Question

Your car's stopping distance, according to a chart in the Alabama Driver's Manual, consists of two parts -- (1) the "thinking distance," the distance you continue to travel at constant velocity during your "reaction time"; and (2) the "braking distance," the distance you travel while actually braking accelerating). (Assume acceleration is constant.) The chart claims, at 65 mph (1 mi/hr = 1.47ft/s), thinking distance is 71 ft and braking distance is 234.7 ft. In determining these numbers,

(A) Find the corresponding reaction time (in seconds) and

(B) braking acceleration in (ft/s^2)

(C) In the "1-second" following-distance rule, it takes one second, at current speed, to cover the distance to the car in front of you. Say that car stopped instantly. According to the above, would a 1-second distance be safe enough, at 65mph? (Remember the thinking distance!)

Explanation / Answer

A )

speed of car = 65 mph = 65 * 1.47 ft / sec = 95.55 ft / sec

thinking distance = speed of car * thinking time

so thinking time t1 = thinking distance / speed = 71/ 95.55 = 0.7430665 secs

B)

braking distance s = 234.7 ft ..

Let accelaration = a

initial velocity = u = 95.55 ft/sec

final velocity = v = 0

v^2 = u^2 + 2*a*s

95.55^2 = 0 + 2 * a * 234.7

so a = - 19.44994 ft/sec2

so braking acceleration = 19.44994 ft / sec2

C )

Let the time taken by car to stop

acceleration = 19.44994 ft / sec2

inia; velocity = 95.55 ft / sec

final velocity = 0

so time taken to retard = 95.5 / 19.44994 = 4.91004085 secs

total time taken = 4.91004085 + 0.7430665 = 5.65310735 secs

now according to 1 second rule .. distance = 71 + 234.7 = 305.7 ft ..

speed = 95.5 ft / sec

so time = 305.7 / 95.5 = 3.201047 secs.....

so it is not safe

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