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The school zone in front of your school has a posted speed limit of 25 mi/h, which is about 11 m/s. Let’s examine the stopping of a car in several different situations.

The driver is looking at her phone and has a total reaction time of 4.6 seconds as the car is moving at a constant speed of 11 m/s. If the driver slams on her brakes and slows down at a rate of -8.2 m/s^2, What is the stopping distance for the car in this situation?

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 Sep 29, 2020
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a total reaction time of 4.6 seconds

   I will assume this means the brakes get applied after 4.6 seconds

      the car will have travelled   4.6 x 11 m/s    before braking = 50.6 m

 

then xf = xo + vo t + 1/2 a t^2     and    vf = vo + at

vf = 0 = 11   -8.2 (t)      solve for t = 1.3415 seconds

xf = xo + vo t + 1/2 at^2

    = 0   + 11 (1.3415)  - 1/2 (8.2)(1.3415^2)

  = 7.38 meters

 

7.38 + 50.6 = 57.98 meters     

 Sep 29, 2020

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