Linear momentum is a fundamental concept in physics that describes the motion of an object. It is a vector quantity, having a magnitude equal to the product of its mass and its velocity, and direction along the object's velocity. On the other hand, linear impulse, also known as momentum impulse, is a concept in physics related to the change in the linear momentum of an object. Impulse is a vector quantity defined as the product of force and the time over which the force is applied.

Delving into the equation of motion for a particle of mass 'm' in an inertial frame, acceleration and velocity are quantified. Integrating this equation over time and rearranging terms yields a formula embodying the principle of linear impulse and momentum. This principle asserts that the sum of the initial momentum of the particle and all applied impulses within a specific timeframe equates to the final momentum. Visualization is facilitated through impulse and momentum diagrams. Momentum diagrams portray the direction and magnitude of initial and final momentum, while the impulse diagram delineates impulses at various points along the particle's path.

To further elucidate, this principle can be translated into three scalar equations by resolving vectors into components. This analytical approach captures the essence of particle dynamics and establishes a foundation for comprehending real-world scenarios involving motion and force interactions.