If acceleration is a function of position, can you express velocity as a function of position, or would there have to be a time variable? For example, if F = kx = ma, and v0 is given, then a = (k/m)x, so what would the function for v be? I would think that, if you know the acceleration at every point along a given path and you know initial velocity, you would also know velocity at every point as well, without having to know what time is. My actual problem is more complicated than a spring, but it comes down to ∫ f(x) d? = ∫ a d? = v, but what would the integral be? dx or dt? Thanks!