Reaction-time Problem # 1

You are driving down the highway late one night at 20m/s when a deer steps onto the road 35 m in front of you. Your reaction time before stepping on the brakes is 0.5s, and the max. deceleration of your car is 10m/s2.

(a) How much distance is between you and the deer when you come to a halt?

(b) What is the max. speed you could have and still not hit the deer?

The minimum stopping distance for a car traveling at a speed of 30 m/s is 60 m, including the time traveled during the driver’s reaction time of 0.50s.

(a) What is the minimum stopping distance for the same car traveling at a speed of 40m/s?

(b) Draw a position-time graph for the motion of the car in part a. Assume the car is at x0=0m when the driver first sees the emergency situation ahead that calls for a rapid halt.

Reaction-time Problem # 2

Problem # 3 A police car chases a speeder who is traveling at

35 m/s. The maximum speed of the police car is 53 m/s. The police car travels from rest with a constant acceleration of 2.2 m/s2 until its speed reaches 53 m/s. It then moves at constant speed. (a) When does the police car catch the speeder if it starts just as the speeder passes? (b) How far has each car traveled?

Problem # 3 contd.

When the police car in the previous problem is traveling at 53 m/s and is 100 m behind the speeder, the speeder sees the police car and slams on the brakes, locking the wheel (resulting in a constant acceleration). Assuming each car can brake at 6m/s2 and the driver of the police car has no reaction time, show that the cars collide. At what time after the speeder applies the brakes do they collide?