Problem from text book: I was driving along at 22 m/s, trying to change a CD and

Question

Problem from text book:

I was driving along at 22 m/s, trying to change a CD and not watching where I was going. When I looked up, I found myself 46 m from a railroad crossing. And wouldn't you know it, a train moving at 30 m/s was only 56 m 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 0.42 s, 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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