Derive `vecF = mvec a` where the symbols have their usual meanings.

Explanation

Newton's II law of motion:
Statement : "The rate of change in the linear momentum of a body is directly proportional to the impressed force and takes place in the direction of force applied.
To Show that `overset(to)(F)=moverset(to)(a).`
Let m be the mass of the body. Let `overset(to) (p_i)` be the initial linear momentum. Let `overset(to)(p_f)` be the final linear momentum as a result of the impressed force.
By definition `underset(Delta t to 0)(lim)(Delta overset(to)(p))/(Delta t)=(doverset(to)(p))/(dt)` where `Deltaoverset(to) (p)=overset(to)(p_f)-overset(to)(p_i) and (doverset(to)(p))/(dt)` is instantaneous acceleration.
From Newton's II law of motion,
`(d overset(to)(p))/(dt) prop overset(to) (F)`
i.e. `overset(to)(F)=k(doverset(to)(p))/(dt)`, where 'k' is a proportionality constant and `overset(to)(p) =moverset(to)(v).`
i.e. `overset(to) (F)=km(doverset(to)(v))/(dt)`, where `(d overset(to)(v))/(dt)=overset(to)(a)` (by definition)
i.e. `overset(to)(F)=kmoverset(to)(a)`
But the magnitude of force `|overset(to)(F)|` is so defined that `k= 1:` We denote `|overset(to)(F)|=m|overset(to)(a)|`
Thus `F= ma and overset(to) (F)=moverset(to)(a)`.