I was driving along at 22 , trying to change a CD and not watching where I was g

Question

I was driving along at 22 , trying to change a CD and not watching where I was going. When I looked up, I found myself 44 from a railroad crossing. And wouldn't you know it, a train moving at 30 was only 56 from the crossing. In a split second, I realized that the train was going to beat me to the crossing and that I didn't have enough distance to stop. My only hope was to accelerate enough to cross the tracks before the train arrived. If my reaction time before starting to accelerate was 0.43 , what minimum acceleration did my car need for me to be here today writing these words?

Explanation / Answer

time taken by train to reach crossing = 56/30 = 1.867s reaction time = 0.42s so, distance covered by car during reaction time s = 0.42*22 = 9.24m let the acceleration required be a(m/s2). distance remaining = 46 - 9.24 = 36.76m time remaining t = 1.867 - 0.42 = 1.447s now s = ut + 0.5at2 =>36.76 = 22*1.447 + 0.5*a*1.447^2 =>a = 4.7m/s2.

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