Can You Calculate the Reaction Time Needed to Avoid a Deer at 18 m/s?

[meggy8716]

A motorist is traveling at 18 m/s^2 when he sees a deer 38 m ahead. If the maximum negative acceleration is -4.5 m/s^2, what is the reaction time (delta t) of the motorist that will allow him to avoid hitting the deer? Answer in units of 's'.

I tried using x(t)=x0+v0t+1/2at^2 and it didn't work out for me. I know the answer is supposed to be 0.1111 s and I can't get this no matter what I try. help!

 

[mjsd]

trying using v = u +at and s = 0.5( u+v) t
and 0.1111s actually is 1/9 or 2/18 or ...

 

[meggy8716]

Mjsd...that makes sense to me except I don't understand why 's' is equal to '1'?? Also, in the s = 0.5 (u+v)t equation I would think that acceleration should be used somewhere in the equation since that is how fast it is decelerating.
My original idea was the use the equation I mentioned above and then use the quadratic equation to get the answer, but that didn't work out so well.

 

[ranger]

Please don't double, triple post the same question.

 

[mjsd]

firstly, let's remember that there are many ways to do the same problem. My way is to do it in two steps. By the way the equations I listed are correct, the second one is just: distance traveled = av. speed x total time.

Logic: how long does it take to stop from initial speed assuming the full $$-4.5m/s^2$$, then in that time how far the vehicle will travel, then what's left for reaction time? etc...