you\'re driving down the highway late one night at 20 m/s when a deer steps onto

Question

you're driving down the highway late one night at 20 m/s when a deer steps onto the road 36 m in front of you. Your reaction time before stepping on the brakes is 0.50 s , and the maximum deceleration of your car is 12 m/s2 .

Problem 2.35 Part A You're driving down the highway late one night at 20 m/s when a deer steps onto the road 36 m in front of you. Your reaction time before stepping on the brakes is 0.50 s and the maximum deceleration of your car is 12 m/s2 . How much distance is between you and the deer when you come to a stop? Express your answer using two significant figures s= 26 Submit My Answers Give Up Incorrect; Try Again; 3 attempts remaining Part B What is the maximum speed you could have and still not hit the deer? Express your answer using two significant figures 2 m/s max = Submit My Answers Give Up

Explanation / Answer

Speed = 20 m/s
a = -12m/sec^2
Distance between car and deer is 36 m

Part A)

TIme taken to stop the car :
V = u + at
0 = 20 - 12*t
t = 20/12
t = 1.67 sec

S = ut +1/2at^2
Hence
S = 20*1.67 + 1/2*(-12)*(1.67)^2
S = 16.667 m

Distance travelled while reacting :
s = 20*.5 = 10 m

Distance between car and deer = 36 - 16.67 - 10 = 9.33 m

part b)
To caluculate maximum speed.

Let maximum speed be v
Then Time taken to stop the car is = v/12 sec

Distance Travelled = v*v/12 - 1/2*12*(v/12)^2
s = v^2/12 - V^2/24
s = V^2/24 m

Distance travelled while reacting : v*(1/2) = v/2 m

Now,
36 = v^2/24 + v/2
v = 24 m/s
Maximum speed can be 24 m/s

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