The \"reaction time\" of the average automobile driver is about 0.7 s . (The rea

Question

The "reaction time" of the average automobile driver is about 0.7 s . (The reaction time is the interval between the perception of a signal to stop and the application of the brakes.) An automobile can slow down with an acceleration of 13.4 ft/s2 .

A.) Compute the total distance covered in coming to a stop after a signal is observed from an initial velocity of 16.4 mi/h . (in a school zone)

B.) Compute the total distance covered in coming to a stop after a signal is observed from an initial velocity of 53.8 mi/h .

Explanation / Answer

Let me do some conversions first.
16.4 m/h = 16.4 * 5280 / 3600 = 24.054 ft/ s
53.8 m/h = 78.907 ft / s

equation:
v^2 = u^2 - 2 a s
where v = final velocity (ft/s); u = initial velocity (ft / s); a = acceleration (ft / s^2); s = distance (ft)
Since it is slowing down, the acceleration is negative.

a) The distance travelled during the reaction time = 24.054 * 0.7 = 16.8378 ft

v = 0; u = 24.054; a = - 13.4 so

0 = 24.054^2 - (2 * 13.4 * s)
s = 24.054^2 / 26.8 = 21.589 ft

So total stopping distance from 16.4 m/h = 21.589 + 16.8378 = 38.4268 ft

b) The distance travelled during the reaction time = 78.907 * 0.7 = 55.2349 ft

v = 0; u = 78.907; a = - 13.4
0 = (78.907)^2 - (2 * 13.4 * s)
s = (78.907^2) / 26.8 = 232.325 ft

So total stopping distance from 53.8 m/s = 232.325 + 55.2349 = 287.56 ft

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.