F = m × a
Mass (m) kg
Acceleration (a) m/s²

Newton's Second Law of Motion

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

F = m × a

Force = Mass × Acceleration

Variables:
  • F = Force (in Newtons, N)
  • m = Mass (in kilograms, kg)
  • a = Acceleration (in meters per second squared, m/s²)
Rearranged Formulas:

m = F / a

Calculate mass when force and acceleration are known

a = F / m

Calculate acceleration when force and mass are known

F = m × a

Calculate force when mass and acceleration are known

Interactive Guide to Newton's Second Law

This law explains how the velocity of an object changes when it is subjected to an external force.

The formula F = m × a means:

  • More force → more acceleration (if mass stays the same)
  • More mass → less acceleration (if force stays the same)
  • To get the same acceleration for a more massive object, you need more force

Everyday Examples:
  • Pushing a shopping cart: The harder you push (more force), the faster it accelerates
  • Car acceleration: More powerful engines (more force) can accelerate the car faster
  • Braking: Applying brakes creates a negative acceleration (deceleration)
Engineering Applications:
  • Rocket design (calculating thrust needed for liftoff)
  • Vehicle safety (designing crumple zones based on deceleration)
  • Sports equipment design (how much force a baseball bat can impart)

Force doesn't cause velocity, it causes changes in velocity (acceleration)
  • An object can move with constant velocity (zero acceleration) with no net force acting on it (Newton's First Law)
  • Force is not something an object "has" - it's something that acts on an object
  • Mass and weight are related but different concepts (weight = mass × gravitational acceleration)
Try It Yourself:

Use the calculator to explore these scenarios:

  1. Calculate the force needed to accelerate a 70 kg person at 9.8 m/s² (equal to gravity)
  2. Find the acceleration of a 1000 kg car with 2000 N of force applied
  3. Determine the mass of an object that accelerates at 5 m/s² when 25 N of force is applied