Tests reveal that a normal driver takes about 0.75 seconds before he or she can

Question

Tests reveal that a normal driver takes about 0.75 seconds before he or she can react to a situation to avoid a collision. It takes about 3 seconds for a driver on a cell phone to do the same. Both drivers are traveling on a straight road at 30 mph (44 ft/s) and their cars can decelerate at 2 ft/s2. Determine the shortest stopping distance d for each vehicle from the moment they see the pedestrians.

Explanation / Answer

First we can find the cars minimum stopping distance: v(t) = 44 - 2*t = 0 => t=22 x(t) = 44*t - (1/2)*2*t^2 x(22) = 484 ft The drivers add an additional distance equal to initial speed times time: 44ft/s * 0.75 seconds = 33 44ft/s * 3 seconds = 132 So add the 484 from the vehicle to both: normal 517 ft drunk 616 ft 2 ft/s^2 is a very unrealistic maximum deceleration for a vehicle, I believe the nhtsa has an expectation of safe 15 ft/s^2 deceleration for roadworthy vehicles, with some cars doing around twice that. For a realistic car, the effect of the increased reaction time would likely nearly double the stopping distance for a drunk as compared to normal.

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