Final answer:
To determine the speed of the train when starting from rest, we can use Newton's second law of motion. The sum of the forces acting on the train equals the mass of the train times its acceleration. The horizontal coupling force at point D between the engine and car A can be calculated using Newton's third law of motion.
Step-by-step explanation:
To determine the speed of the train when starting from rest, we can use Newton's second law of motion. The sum of the forces acting on the train equals the mass of the train times its acceleration. Since the train starts from rest, its initial velocity is zero. Therefore, the only force acting on the train is the traction force provided by the tracks. We can calculate the acceleration using the formula F = ma, where F is the traction force and m is the mass of the train. Once we have the acceleration, we can use the kinematic equation v = u + at to calculate the speed of the train, where v is the final velocity, u is the initial velocity (which is zero), a is the acceleration, and t is the time it takes for the train to reach that speed.
Now, to determine the horizontal coupling force at point D between the engine and car A, we can use Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. The force exerted by the engine on car A is equal in magnitude and opposite in direction to the force exerted by car A on the engine. This force can be calculated using the equation F = ma, where F is the force exerted by car A on the engine, m is the mass of car A, and a is the acceleration of the train.
Given the masses of the engine and cars, we can now calculate the acceleration of the train using the formula F = ma. Since all the cars are connected, the acceleration of the entire train is the same. Once we have the acceleration, we can use it to calculate the speed of the train and the coupling force at point D.