Halliday, Resnick & Walker — Motion Along a Straight Line: Problem 102

Car-following stopping distance. When you drive behind another car, what is the minimum distance you should keep between the cars to avoid a rear-end collision if the other car were to suddenly stop (it hits, say, a stationary truck)? Some drivers use a “2 second rule” while others use a “3 second rule.” To apply such rules, pick out an object such as a tree alongside the road. When the front car passes it, begin to count off seconds. For the first rule, you want to pass that object at a count of 2 s, and for the second rule, 3 s. For the 2 s rule, what is the resulting car−car separation at a speed of (a) 15.6 m/s (35 mi/h, slow) and (b) 31.3 m/s (70 mi/h, fast)? For the 3 s rule, what is the car−car separation at a speed of (c) 15.6 m/s and (d) 31.3 m/s? To check if the results give safe trailing distances, find the stopping distance required of you at those initial speeds. Assume that your car’s braking acceleration is –8.50 m/s² and your reaction time to apply the brake upon seeing the danger is 0.750 s. What is your stopping distance at a speed of (e) 15.6 m/s and (f) 31.3 m/s? (g) For which is the 2 s rule adequate? (h) For which is the 3 s rule adequate?