You\'re driving down the highway when a deer steps onto the road 35m in front of

Question

You're driving down the highway when a deer steps onto the road 35m in front of you. Your reaction time before stepping on the breaks is 0.5 seconds and the deceleration of the car is 10 m/s^2. What is the maximum speed that you could have and still not hit the deer? The above solution is incorrect.
Here is how I interpreted the problem.
              entire distance is 35 meters
I--------------------------------------------------I
t=0              t=0.5                       t=? I--------------------I-----------------------------I
   "coasting"     ^begins deceleration
The answer should be ~21.5 m/s but I am not sure how to prove this
You're driving down the highway when a deer steps onto the road 35m in front of you. Your reaction time before stepping on the breaks is 0.5 seconds and the deceleration of the car is 10 m/s^2. What is the maximum speed that you could have and still not hit the deer? The above solution is incorrect.
Here is how I interpreted the problem.
              entire distance is 35 meters
I--------------------------------------------------I
t=0              t=0.5                       t=? I--------------------I-----------------------------I
   "coasting"     ^begins deceleration
The answer should be ~21.5 m/s but I am not sure how to prove this

Explanation / Answer

Step-by-step: 1) identifying: d = 35m, t = 0.5 s, a = -10m/s^2, vi = ? , vf = 0m/s 2) Use formulae: d = (vi)t + (1/2)at^2 ------> 35m = (vi)(0.5) + (1/2)(-10)(0.5^2) ---------> [35 - (1/2)(-10)(0.5^2)]= (vi)(0.5) ---------> vi = [35 - (1/2)(-10)(0.5^2)] /0.5 ---------> vi = 67.5m/s

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