A book is lying on the table. It is at rest. Its velocity is 0 and uncertainty in velocity $\Delta v$ is 0. Does this mean that uncertainty in its position is ∞?
Leaving the math aside, the uncertainty principle must be taken into account when dealing with very, very small objects. the larger the object becomes, the smaller the effects of this principle become. For macroscopic objects like books and people, the uncertainty principle produces effects that are far too small to detect even with the most sensitive instruments. So in your example, you do not have to worry about having the position measurement of the book affecting the velocity measurement of it.
You are confusing macro- and micro-scales here. Your book moves on a microscopic scale. And the uncertainty in its position is also on a scale that you cannot detect with your eyes. Be careful when transfering quantum phenomena to everyday experiences. Your measurement apparatus might not be suitable ;)