Question

How do I find velocity and acceleration as functions of `t`?

Answer 1

See below.

Explanation:

It depends on the nature of the motion you're studying. For example, if a body moves with constant velocity, you will have `v=s/t`, and `a=0`.
On the other hand, if a body moves with constant acceleration, you will have `v = at` and `a = k` (some constant).

In general, the only thing you can say is that, if you know the function `s(t)` that gives the position `s` at every time `t`, you will have that the velocity is the first derivative of `s`, and the acceleration the second derivative.