In senior two mathematics, it is known that the distance s is a function of time t: s=s(t).

After a period of △t at t, the corresponding distance is s(t+△t).

So the distance △t in time is s(t+△t)-s(t)=△s, and its average speed = △ s/△ t.

When the time is △t→0, the limit of the average speed is the instantaneous speed at t.