Newton's Second Law states that a physical object's acceleration is proportional, by a factor of the objects mass, to the force imparted upon it. Algebraically, it can be written as where is the net force imparted on the object, is its mass, and 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 .
Rate of change of a quantity (lets say $x$) is defined as where $t$ is time, and $\Delta t$ represents change in time.
if we use definition, then mathematically second law is equivalent to
We can further simplify this differentiation using chain rule
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.