A locomotive is dragging empty freight cars, while coal is being dropped into them. It’s falling down into those freight cars with an efficiency (μ). Overall mass of the whole empty train is M.

a) Calculate v(t) (velocity with respect to time), assuming that the force of train engine and the force of friction are constant.

b) Calculate v(t), assuming that at the moment the coal started dropping, the train engine was stopped. Assume that to drag the empty train a power (P) is needed, and the resultant force of friction remains constant. After what time (t

0) will the train stop?

c) What additional force (F

c) needs to be used so that during the coal dropping the velocity of train doesn’t change and equals v

0?

I have no idea how to tackle it. After searching for hours i found this (variable-mass system equation):

but I'm still left clueless.

Thank you for help.