Question

We want to construct a formula for the acceleration

Answer 1

As long as there are no other specifications or details regarding the question, I can give some general recommendations how the expression for acceleration can be obtained (assuming that we consider a point mass):

1) if this is a problem in kinematics, the corresponding expression can be obtained by means of differention of the law of motion over time twice, i.e.

$$\vec{a} (t) = \frac{d^2 \vec{r}}{dt^2} \equiv \ddot{\vec{r}}$$

or if the velocity is known then

$$\vec{a} (t) = \frac{d \vec{v}}{dt} \equiv \dot{\vec{v}}.$$

2) in dynamics one should obtain the net force acting on the body (a point mass) and use the 2nd Newton's law:

$$\vec{a} = \frac{\vec{F}}{m}.$$