How does reactivity relate to the periodic table

For metals:
- Reactivity increases as you go down a group, the further you go down, the easier the metals take or give electron
- Reactivity decreases as you go across, more energy required to get rid of valence electron

For non-metals:
- Reactivity increases as you go up a group. Electronegativity increases as you go higher up, more powerful exchange of electrons
- Relativity increases as you go across since the closer you get to fill up your s- and p- orbitals the more motivated you are to do so.

Does this your question?

Is a  vector quantity  that refers to "the rate at which an object changes its position." imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. while this might result in a frenzy of activity, it would result in a zero velocity. because the person always returns to the original position, the motion would never result in a change in position. since velocity is defined as the rate at which the position changes, this motion results in zero velocity. if a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. every step must go into moving that person further from where he or she started. for certain, the person should never change directions and begin to return to the starting position.