This part of the problem applies to any road surface, so the value of h is not known. Suppose you are driving at 70 miles per hour but, because of approaching darkness, you wish to slow to a speed that will cut your emergency stopping distance in half. What should your new speed be?

v₀ = 49.5 miles / h

Explanation:

We can solve this exercise with kinematics in one dimension

v² = v₀² - 2 a d

let's apply this equation to the initial data, the fine velocity zero

0 = v₀² - 2 a d

a = v₀² / 2d

in the second case the distance is half (d' = ½ d), the acceleration of the vehicle is the same, we look for the initial speed

0 = v₀'² - 2 a d'

v₀'² = 2 a d = 2 (v₀² / 2d) d'

v₀' = v₀ √ 1/2

let's calculate

v₀' = 70 ra 0.5

v₀ = 49.5 miles / h