Halliday, Resnick & Walker — Force and Motion–II: Problem 75

A locomotive accelerates a 25-car train along a level track. Every car has a mass of \(5.0 \times 10^4 \text{ kg}\) and is subject to a frictional force \(f = 250v\), where the speed \(v\) is in meters per second and the force \(f\) is in newtons. At the instant when the speed of the train is \(30 \text{ km/h}\), the magnitude of its acceleration is \(0.20 \text{ m/s}^2\). (a) What is the tension in the coupling between the first car and the locomotive? (b) If this tension is equal to the maximum force the locomotive can exert on the train, what is the steepest grade up which the locomotive can pull the train at \(30 \text{ km/h}\)?