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 46 m from a railroad crossing. And wouldn't you know it, a train moving at 29 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?

Answer 1

6.46393559312 m/s²

Step-by-step explanation:

Time taken to cover 56 m

`t=(56)/(29)\ s`

Distance covered in 0.42 seconds

`0.42* 20=8.4\ m`

From equation of linear motion

`s=ut+(1)/(2)at^2`

`8.4+20((56)/(29)-0.42)+(1)/(2)a((56)/(29)-0.42)^2=46\\\Rightarrow a=(46-8.4-20((56)/(29)-0.42))*(2)/(((56)/(29)-0.42)^2)\\\Rightarrow a=6.46393559312\ m/s^2`

The minimum acceleration is 6.46393559312 m/s²