AN INSIGHT INTO THE NEWTON'S SECOND LAW OF MOTION

WHAT WE ASSUME:-

Applying a force on a body causes a body's velocity to change and results in a non-zero acceleration which is in the direction of force. This is governed by the famous formula, F=m.a

WHAT IT ACTUALLY IS:-

Newton's second law of motion can be more fundamentally stated as the follows: The rate of change of momentum of an object is directly proportional to the applied force on the object and the change in momentum takes place in the direction of the applied force. This is shown by the formula- 

where "F" is the force acting on the body, "p" is the momentum and "t" is the time.

This formula can be further extended as- 

This is also logical and important to know because many people (including many high school students) have this major misconception. This is because, velocity and force are related to each other directly. The main effect of force is that it changes the quantity of Force is related to momentum directly because momentum is none other than the quantity of motion present in the body. Changing the momentum means that the amount of motion in the body is changing, hence an external unbalanced force is acting on the body. 

Another way to analyze the above situation is by seeing it through the cause-effect theory. Let's take a block which has a mass of "m" kg, initial velocity "u" m/s, which is moving across a smooth floor as shown. 

Now we apply an external unbalanced force "F" in the direction of the initial velocity for a time period "t". This causes an increase in the velocity of the block. 

If we analyze this situation by the cause-effect theory, then we can say that the "Force" is the cause and the "Change in Velocity" is actually the "effect". Hence, the relation of force is more justified with velocity and not with acceleration. That is why the most fundamental equation of the Newton's 2nd law is in terms of momentum and not acceleration.