by sga
--- original
+++ modified
@@ -3,3 +3,15 @@
\vec F = m\vec a
$$
where $$\vec F$$ is the net force imparted on the object, $$m$$ is its mass, and $$\vec a$$ its acceleration.
+
+In its most basic (or general) form, the law states _force acting on a object is directly proportional to rate of change of it's momentum_.
+
+For a object, its _linear momentum_ $P$ is defined as $$\vec P = m \vec v$$.
+
+Rate of change of a quantity (lets say $x$) is defined as $$ \lim_{\Delta t \rightarrow 0} \frac{\Delta x}{\Delta t} = \frac{d x}{d t} $$ where $t$ is time, and $\Delta t$ represents change in time.
+
+if we use definition, then mathematically second law is equivalent to $$ \vec F = \frac{\Delta \vec p}{\Delta t} $$
+
+We can further simplify this differentiation using chain rule $$ \vec F = m\frac{\Delta \vec v}{\Delta t} + \vec v \frac{\Delta m}{\Delta t} $$
+
+Usually mass of a object $m$ is a constant, and hence we usually neglect the latter term in above equation (it would be 0), but when mass of a object changes, then we can not ignore it, for example _rocket propulsion_. Rockets work by burning a fuel, which produces a lot of energy, which in turn gives the end products of the reaction to move fast. By carefully designing, we can have the end products leave in a certain direction, which will have some velocity. Equivalently, our rocket lost some mass (fuel stored in some tanks) which left with some velocity, and hence the second terms gives us the force of _thrust_.