An inattentive driver is travelling 18m/s. When he notice a red light ahead. His car is capable of a breaking acceleration of 3.65m/s^2. If it takes him 0.200 second to get the brakes on and he is 45m from the intersection when he sees the ligth, will he be able to stop in time?

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  1. just plug in your numbers into the equation of motion:
    how long does it take to stop (v=0)?
    v = 18 - 3.65t
    t = 4.932
    How far does he go?
    s = vt + 1/2 at^2
    s = 18t - 1.825t^2
    time to stop: 4.932+0.200 = 5.132 seconds
    s = 18*5.132 - 1.825*5.132^2 = 44.310
    >whew< close call!

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  2. V^2 = Vo^2 + 2a*d = 0.
    324 + (-7.30)d = 0,
    d = 44.4 m = stopping distance.

    45 - 18m/s * 0.2s = 41.4 m. = Required stopping distance.
    No, he will not be able to stop in time.

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