newtonian mechanics - How force is equal to the product of mass and instantaneous acceleration?

$$\vec{F}=m\vec{a}$$ Suppose that an object of some mass was constantly accelerating ($\vec{a} \neq 0$) through sometime interval. With no doubt, the object had an instantaneous acceleration at any instant in that time interval (since the instantaneous acceleration is defind as a limit).

What about the force? How can there occur a force at a specific time (for example, at $t=2s$)? Since a specific time is not a time interval the force can spend acting on the object!
What I think of is that forces must spend time intervals acting on objects, so, there can not be a force without a time interval, so how (if there is no force at a specific time) there is an acceleration?