Newton’s Three Laws of Motion: Comprehensive Principles, Formulae, and Solved Numericals

Newton’s First Law states: ‘A body continues its state of rest or of uniform motion in a straight line unless acted upon by an external unbalanced net force.’ This property of matter to resist any change in its existing state of motion is termed inertia. Inertia is directly proportional to mass; a heavier vehicle requires far greater force to accelerate or halt than a bicycle.

When an unbalanced force F acts on a body of mass m, it produces an acceleration a in the direction of the force:

• Acceleration is directly proportional to the applied force: a ∝ F
• Acceleration is inversely proportional to mass: a ∝ 1/m

Combining both proportionalities yields: F = ma. In the SI system, Force is measured in Newtons (N), where 1 N = 1 kg·m/s².

Newton’s Third Law states: ‘To every action, there is always an equal and opposite reaction.’ Crucially, action and reaction forces always act on two different interacting bodies, meaning they never cancel each other out. Everyday examples include walking on pavement, swimming, and rocket propulsion where expelled exhaust gases push the rocket skyward.

Question: Calculate the force required to accelerate a 1200 kg car from rest to a velocity of 20 m/s in 5 seconds.

Solution:
Given: m = 1200 kg, v_i = 0 m/s, v_f = 20 m/s, t = 5 s.
Using First Equation of Motion: a = (v_f – v_i) / t = (20 – 0) / 5 = 4 m/s².
Applying Newton’s Second Law: F = ma = 1200 × 4 = 4,800 N.
Answer: The required accelerating force is 4,800 Newtons.