newtonian mechanics - What is function of force $F$ and work $W$?

I know that :

Position

$$r:\mathbb{R} \to\mathbb{R^3} \ \ \ \ \ ; \overrightarrow{r}(t)$$

Velocity

$$v :\mathbb{R} \to\mathbb{R^3} \ \ \ \ \ ; \overrightarrow{v}(t)$$

Acceleration

$$a:\mathbb{R} \to\mathbb{R^3} \ \ \ \ \ ; \overrightarrow{a}(t)$$

Now i want to know that , what is function of force $F$ and work $W$ ?