Use of Calculus in Newtons Laws

[Vorde]

Why do I see Newtons 3 laws (mostly 2 and 3) given using differentials (F=dp/dt etc...) when it is far simpler to use the basic form F=ma (and the same for the 3rd law), is there an advantage to the more complicated form?

 

[Pi-Bond]

The differential form is the general law. F=ma only follows if the mass remains constant.

$F=\frac{d(mv)}{dt}=m\frac{dv}{dt}$

However all physical situations do not have constant mass. So the differential form has the advantage of generality.

 

[Vorde]

That makes sense, thank you.