State Newton’s second law of motion. Derive a mathematical formula in terms of acceleration.

Newton’s second law of motion explains how the motion of an object changes when a force is applied to it. The law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

Statement of the Law

In simple terms, this means that the greater the force applied to an object, the more it will accelerate. Conversely, heavier objects require more force to achieve the same acceleration as lighter ones.

Mathematical Representation

The mathematical formula that represents this relationship is:

• F = m × a

Where:

• F = net force applied (in Newtons)
• m = mass of the object (in kilograms)
• a = acceleration (in meters per second squared)

Deriving the Formula

To derive the formula, consider the following steps:

1. Start with the definition of acceleration: a = Δv / Δt, where Δv is the change in velocity and Δt is the change in time.
2. According to Newton’s second law, the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
3. Rearranging the equation gives us a = F / m, showing how acceleration depends on force and mass.

This relationship is fundamental in physics, illustrating how forces affect the motion of objects in our everyday lives.