I think the whole thing can be explained in terms of clsses/sets.
The sum of numbers of elements in subsets/subclasses will represent
number of elements in the parent set /class.
When apples and oranges are added we get number of fruits.
Of course you can add numbers from any absolutely unrelated sets/classes
and you will still get a number which belongs to sets of all sets/ class
of all classes.
When you devide the elements of set/class of length by elements of
set/class of time, you get the elements of the set/class of velocity.
Similarly for acceleration. You have a set/class of mass. So also there
is a set/class of force.
Physics tells that you get elements of the set/class of force when
you multiply the elements of set/class of mass with the elements
of set/class of acceleration.