You are driving down the highway late one night at 20m/s when a deer steps onto

Question

You are driving down the highway late one night at 20m/s when a deer steps onto the road 35m in front of you. Your reaction time before stepping on the brakes is 0.50s , and the maximum deceleration of your car is 10m/s^2 . How much distance is between you and the deer when you come to a stop? I KNOW THE ANSWER IS 35-30= 5M, BUT I NEED TO KNOW THE ANSWER TO THE SECOND PART OF THE QUESTION WHICH IS THIS : You found the distance that you will cover while braking(5M). You can use the expected amount of time for braking to check your answer for distance.
Using the information given in the introduction and the value for distance that you found above, determine the time required for you to stop once you press the brakes. Note that the time for braking is just the time interval t3-t2. and answer it in SECONDS. Thank you!!!! (I believe t2 is 0.50seconds.)

Explanation / Answer

Distance traveled in 0.5 s = 10m

Distance traveled under deceleration

= v^2 / 2 a = 20^2 / 20 = 20 m

Total distance traveled before stopping = 30m..... 5m from the deer.

Distance traveled under deceleration = v^2 / 20

v^2 / 20 + 0.5v = 35

v^2 + 10 v = 700

Solve this quadratic

v = 21.925 m/s

= 22 m/s

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