An engineering student claims that a country road can be safely negotiated at 65 mi/h in rainy weather. Because of the winding nature of the road, one stretch of level pavement has a sight distance of only 510 ft. Assuming practical stopping distance, comment on the student

Negotiated speed should be lower. Perception/reaction time is too less than design values.

Explanation:

Given:

- The claimed safe speed V_1 = 65 mi/h

- Sight distance D = 510 ft

- The practical deceleration a = 11.2 ft/s ... according to standards

Find:

Assuming practical stopping distance, comment on the student whether the claim is correct or not

Solution:

- Calculate the practical stopping distance:

d = V_1^2 / 2*a

d = (65 * 1.46) ^2 / 2*11.2 = 402.054 ft

- Solve for reaction distance d_r is as follows:

d_r = D - d = 510 - 402.054 = 107.945 ft

- The perception/time reaction is:

t_r = d_r/V_1 = 107.945 / 94.9

t_r = 1.17 sec

Answer: The perception/reaction time t_r = 1.17 s is well below the t = 2.3 s.

Hence, the safe speed should be lower.