# Newton’s laws of motion: Mathematical expressions

The three laws of motion formulated by Sir Isaac Newton are fundamental principles that govern the motion of objects. These laws, when combined with mathematical expressions and practical examples, provide a comprehensive understanding of how objects behave when forces act upon them.

1. Newton’s First Law of Motion – The Law of Inertia:
Newton’s first law states that an object at rest will remain at rest, and an object in motion will continue moving at a constant velocity unless acted upon by an external force. Mathematically, it can be expressed as:
F = ma = 0

Here, F represents the net force acting on the object, m is the mass of the object, and a is its acceleration. When the object is at rest or moving with a constant velocity, the acceleration is zero, implying that the net force acting on the object is also zero.

For example, imagine a book lying on a table. Without any external force acting on it, the book remains at rest. Once a force, such as a push or pull, is applied to the book, it overcomes the inertia of the object, causing it to move.

2. Newton’s Second Law of Motion – The Law of Acceleration:
Newton’s second law describes the relationship between the net force acting on an object, its mass, and its resulting acceleration. Mathematically, it can be expressed as:
F = ma

In this equation, F represents the net force, m is the mass, and a is the acceleration of the object. This law indicates that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

For instance, consider a car with a mass of 1000 kg. If a net force of 500 N is applied to the car, we can calculate its acceleration using Newton’s second law:
F = ma
500 = 1000a
a = 0.5 m/s^2

Thus, the car will accelerate at a rate of 0.5 m/s^2 under the influence of this force.

3. Newton’s Third Law of Motion – The Law of Action and Reaction:
Newton’s third law states that for every action, there is an equal and opposite reaction. Mathematically, it can be expressed as:
F1 = -F2

In this equation, F1 represents the force exerted by object 1 on object 2, and -F2 represents the force exerted by object 2 on object 1. These forces are equal in magnitude but act in opposite directions.

For example, when you push a wall, you exert a force on the wall. Simultaneously, the wall exerts an equal and opposite force back on you, preventing you from moving through the wall.

Overall, these three laws of motion, when combined with mathematical expressions and practical examples, allow us to understand and predict the behavior of objects in response to various forces and interactions. By unraveling the mysteries of motion, Newton’s laws have revolutionized the field of physics and continue to be cornerstones of our understanding of the physical world.