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free fall trajectory in non constant gravitational field

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Rusty on the math...
I am working on a problem and need the derivation of a free fall trajectory for an object at a distance above earth where the change in acceleration is not negligible. How do I integrate the distance/ acceleration formula taking into account the change in g to get the total distance traveled.
The method and final formula...?
I'm looking for total distance after time t, trying to see how it scales as what power of t.
thanks.

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