Halliday, Resnick & Walker — Force and Motion–II: Problem 101

Controlled platoon of cars. A platoon of cars moves along a road under computer control with uniform spacings and equal speeds that are set by a dynamic system that monitors the weather road conditions. It determines the speed for a given spacing such that, in an emergency, each car would stop just as it reached the car in front of it. The coefficient of static friction \(\mu_s\) is 0.700 for dry asphalt and 0.300 for rain-wetted asphalt. The cars each have length \(L = 4.50 \text{ m}\). What should the controlled speed be (meters per second, miles per hour, and kilometers per hour) if the bumper–bumper spacing is \(2L\) for (a) dry asphalt and (b) wet asphalt? What should it be if the spacing is \(5L\) for (a) dry asphalt and (b) wet asphalt?