You're driving down the highway late one night at 20 m/s when a deer steps onto the road 35 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 10 m/s^2
a. How much distance is between you and the deer when you come to a stop?
b. What is the maximum speed you could have and still not hit the deer?

1 Answers

Best Answer

Step 1
Given data
Our driving speed is u = 20 m/s.
The distance between the car and the deer is d_b = 35 m
The reaction time interval is t = 0.50s .
The deceleration rate of car is a = - 10 m/s^2 .
a) The distance traveled by car in the reaction time as,
u = d/t
d_1 = ut
d_1 = 20 m*0.5 s
d_1 = 10 m
Step 2
The distance required to stop the car due to deceleration as,
v^2 = u^2 + 2 ad_2
0 = (20 m/s)^2 + 2*(-10 m/s^2)*d_2
d_2 = 400/20
d_2 = 20 m
The total distance traveled by car before car stops is;
d_2 = d_1 + d_2
d_1 = 10 m + 20 m
d_1 = 30 m
Therefore, the distance between car and deer after car stop is calculated as,
d = d_b - d_t
d = 35 m - 30 m
d = 5 m
Thus, the distance between the car and the deer is 5 m.