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?
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.