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1 November, 09:48

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?

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  1. 1 November, 11:53
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    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
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