Dependence between Variables
We are not really interested in changing of one variable, it is more interesting to study dependence between two variables when they both change.
Such variables can not take simultaneously any pair of values: if one of them (independent variable) is given certain value, then we can find value of second variable (dependent variable).
For example, area `A` of circle is function of its radius `r`: `A=pi r^2` i.e. we can find area of circle given radius. When radius `r=2` then area of circle `A` equals `A=4pi`.
In a case of free fall of particle without air resistance time `t` (in seconds) counted from start of movement and distance `s` (in meters) travelled are connected by equation `s=1/2 g t^2`, where `g=9.81 (m)/(s^2)` is constant. Here we can find what distance particle traveled given time, in other words `s` is function of time `t`.
Note, that here choice of independent variable from given two is often indifferent. Choice of independent variable depends on what variable we want to investigate.
For example, area of circle is function of radius: `A=pir^2`, but rewriting this equation makes radius function of area, in other words area becomes independent variable: `r=sqrt(A/pi)`.