Final answer:
The power exerted on the train during its ascent cannot be calculated without the time duration for its travel over the 5.0 km track with a vertical rise of 40 m. Power is the rate of doing work over time, and since the problem does not supply the necessary time information, the calculation cannot be completed.
Step-by-step explanation:
To evaluate the power exerted on a train during its movement up a vertical rise, the work-energy principle can be applied along with the definition of power as work done over time. The work done can be calculated by considering both the change in potential energy (due to the vertical rise) and the change in kinetic energy (due to the change in speed). The power can then be isolated by dividing the total work calculated by the time taken to perform it.
However, as the problem does not provide the time duration for this process, one critical piece of information needed to calculate power is missing. Power is defined as the rate of doing work or energy transfer per unit of time, and with the given data, the calculations cannot be completed without the time factor. Therefore, the power output for the train in this scenario cannot be determined from the information provided, as we require the time taken to travel the 5.0 km stretch of track at the described conditions.