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I haven't covered differential equations yet and was wondering if this is an example of a kind of problem that subject deals with.

For example,

Let's say the particle moves with A(x)=M/X^2

taking d(A)/d(x) can give the change in Acceleration at any distance x, but what about time?

In calc 1 we did some 'related rates' problems that were similar to this, but they always had a special relationship that let you solve it (right triangles etc).

So: how do you solve this case in particular, what subject matter deals with this, and where can I get more info on other questions like it?

Thanks for the help! :)