Halliday, Resnick & Walker — Motion Along a Straight Line: Problem 94

Car lengths in trailing. When trailing a car on a highway, you are advised to maintain a trailing distance that is often quoted in terms of car lengths, such as in “stay back by 3 car lengths.” Suppose the other car suddenly stops (it hits, say, a large stationary truck). Assume a car length \( L \) is 4.50 m, your car speed \( v_0 \) is 31.3 m/s (70 mi/h), your trailing distance is \( nL = 10.0L \), and the acceleration magnitude at which your car can brake is 8.50 m/s\(^2\). What is your speed just before colliding with the other car if (a) your reaction time \( t_r \) to start braking is 0.750 s and (b) automatic braking is immediately started by your car’s radar system that continuously monitors the road? What is the minimum value for \( n \) needed to avoid a collision with (c) the reaction time \( t_r \) and (d) automatic braking?