Answer: It remains the same
Explanation:
The Conservation of Momentum principle establishes that the initial momentum [tex]p_{o}[/tex] must be equal to the final momentum [tex]p_{f}[/tex]:
[tex]p_{o}=p_{f}[/tex] (1)
In the case of the train, its initial momentum is:
[tex]p_{o}=m_{train}V_{train}[/tex] (2)
Where [tex]m_{train}[/tex] is the mass of the train and [tex]V_{train}[/tex] is the initial velocity of the train
And, its final momentum is:
[tex]p_{f}=(m_{train}+m_{coal})V_{train+coal}[/tex] (3)
Where:
[tex]m_{train}+m_{coal}=2m_{train}[/tex] since we are told the mass of the train is doubled
[tex]V_{train+coal}=\frac{1}{2} V_{train}[/tex] since we are told the velocity of the train goes to half
Hence:
[tex]p_{f}=2m_{train}\frac{1}{2} V_{train}[/tex] (4)
[tex]p_{f}=m_{train}V_{train}[/tex] (5)
[tex]m_{train}V_{train}=m_{train}V_{train}[/tex] (6)
[tex]p_{o}=p_{f}[/tex]
This means the momentum of the train remains the same.
