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Is it possible to derive velocity vector form position vector without unknown such as: position vector of A = (0.8)i + (1.2)j?

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  • $\begingroup$ Welcome to Engineering! Before answering, it'd be useful if you could expand on the example given. What are $A$, $i$ and $j$? Is this describing the path of the object? If so, this would mean $i$ and $j$ are related to one another (since the object can only be in one point along the path at any given time. Or are $i$ and $j$ simply the unit vectors for the x- and y- axes? If the latter, then the already-given answers are correct, since you'd need some way to tie position to time to derive the velocity. $\endgroup$ – Wasabi Nov 21 '19 at 0:22
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Simple answer is that you can't because you have to take derivative of the position vector with respect to time which would be zero in the case of the vector you described (It simply doesn't contain the temporal information).

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If you only have a general postion vector that describes the path of the object, then it's impossible to derive the velocity vector. Here I try to demonstrate it:

Since the point masses are dimensionless, we can consider two different point masses at the exact same location. Point mass $m_1$ moves with velocity $v_1$ so the point mass $m_2$ with $v_2$, those masses share the same location but move with different speeds.

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