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Momentum of Freight car containing a mass of sand

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A freight car of mass M contains a mass of sand "m". At t=0 a constant horizontal force F is applied in the direction of rolling and at the same time a port in the bottom is opened to let the sand flow out at constant rate dm/dt.

Find the speed of the freight car when all the sand is gone. Assume the freight car is at rest at t=0

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We can start w/ Newton's law F=ma

But in this case "m" is the mass of the car and the sand

We should write this as...

The mass of the sand lost is ...

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