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 12.0 ft/s2 . Part A Compute the total distance covered in coming to a stop after a signal is observed from an initial velocity of 13.4 mi/h . (in a school zone) Part B Compute the total distance covered in coming to a stop after a signal is observed from an initial velocity of 57.2 mi/h .

Explanation / Answer

Given:-
13.4 mi/hr =5.990 m/s
& 57.2 mi/hr = 25.57 m/s
& 12 ft/sec^2 = 3.66 m/s^2
(a) distance covered in reaction time(s1) by s = ut
=>s1 =5.990 x 0.7 = 4.193 m
distance covered after applying brakes (s2) by v^2 = u^2 - 2as
=>0 = (5.990)^2 - 2 x 3.66 x s2
=>s2 = 4.901 m
=>Total stopping distance (s) = s1+s2 = 9.094 m

(b) distance covered in reaction time(s1) by s = ut
=>s1 =25.57 x 0.7 = 17.89 m
distance covered after applying brakes (s2) by v^2 = u^2 - 2as
=>0 = (25.57)^2 - 2 x 3.66 x s2
=>s2 = 89.32 m
=>Total stopping distance (s) = s1+s2 = 107.21 m

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