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10 January, 04:54

If a car is speeding down a road at 40 miles/hour (mph), how long is the stopping distance d40 compared to the stopping distance d25 if the driver were going at the posted speed limit of 25 mph?

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  1. 10 January, 05:17
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    Assume that the deceleration due to braking is a ft/s².

    Note that

    40 mph = (40/60) * 88 = 58.667 ft/s

    25 mph = (25/60) * 88 = 36.667 ft/s

    The final velocity is zero when the car stops, therefore

    v² - 2ad = 0, or d = v² / (2a)

    where

    v = initial speed

    a = deceleration

    d = stopping distance.

    The stopping distance, d₄₀, at 40 mph is

    d₄₀ = 58.667² / (2a)

    The stopping distance, d₂₅, at 25 mph is

    d₂₅ = 36.667² / (2a)

    Therefore

    d₄₀/d₂₅ = 58.667² / (2a) : 36.667² / (2a)

    = (58.667/36.667) ²

    = 2.56

    Answer:

    The stopping distance at 40 mph is 2.56 times the stopping distance at 25 mph.
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