I was driving along at 20 m/s, trying to change a CD and not watching where I wa

Question

I was driving along at 20 m/s, trying to change a CD and not watching where I was going. When I looked up, I found myself 43 m from a railroad crossing. And wouldn't you know it, a train moving at 30 m/s was only 60 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 0.46 s , what minimum acceleration did my car need for me to be here today writing these words?

I did it by solving a from Vi*t+.5*a*t^2<=43 in which t=2s-0.46s=1.54s, Vi=20m/s but still didnt get the right answer, please help me on that

Explanation / Answer

here

time it will take train to reach crossing is = 60 / 30 = 2 sec

the reaction time is 0.46 sec

in the time you have travelled 0.46 * 20 = 9.2 m

then your distance form crossing is = 43 - 9.2 = 33.8 m

the time left for crossing is = 2 - 0.46 = 1.54 sec

then by using the second equation of motion

y = u *t + 0.5 *a *t^2

33.8 = 20 * 1.54 + 0.5 * a * 1.54^2

a =( 33.8 - (20 * 1.54) )/ ( 0.5 * 1.54^2)

a = 2.53 m/s^2

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