You'll want to know something about finite differences in order to do this.
A single discrete value is insufficient.
A first order derivative w.r.t. time would look like this:
da/dt(t) ~ (a(t+dt)-a(t))/dt
d^2a/dt^2(t) ~ (da/dt(t+dt)-da/dt(t))/dt
(I could make this easier to read if I had LaTeX.)
You can use other formulas, but these are simplest.
The ideas are commonly understood from differential calculus.