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A particle moves from point A to point B in one dimension. The velocity of the particle changes with position according to some formula V = V(x). How long does it take for the particle to get from point A to point B?

If I could write V as a function of time, I could than integrate V=V(t) from 0 to t and that would give me the transit time. How do I do it if V depends on X?

Say, for example, V(X) = 1 + ax