Newton's Second Law
Simple Explanation
Newton's second law says the acceleration of an object is directly proportional to the net force acting on it, and inversely proportional to its mass: F = ma. A bigger force gives a bigger acceleration; a bigger mass gives a smaller acceleration, for the same force.
Why Do We Need It?
This law is the single most useful equation in all of mechanics — it connects force, the quantity that causes motion to change, directly to the motion itself.
Formula
Newton's Second Law
F = ma
The net (resultant) force acting on an object equals its mass times its acceleration. A bigger force produces a bigger acceleration; a bigger mass resists acceleration more, for the same force.
- F
- — net force acting on the object, in newtons (N)
- m
- — mass of the object, in kilograms (kg)
- a
- — acceleration produced, in metres per second squared (m/s²)
When to use it: Whenever a net force and a mass are known and the resulting acceleration is needed (or any one of the three, given the other two).
Worked Example
Find a crate's acceleration
A net force of 60 N acts on a crate of mass 12 kg. Find its acceleration.
Why Does This Work?
This law defines exactly how force and mass together determine acceleration; rearranging it to solve for whichever quantity is unknown always works, as long as the other two are known.
Real-Life Example
Why a loaded truck accelerates more slowly
A truck's engine applies the same force whether the truck is empty or fully loaded.
Because the loaded truck has a much greater mass, the same engine force produces a much smaller acceleration — exactly as F = ma predicts.
Practice
A net force of 45 N gives a trolley an acceleration of 3 m/s². Find the mass of the trolley.
MediumA mass of 8 kg is accelerated at 2.5 m/s². Find the net force required.
MediumCommon mistake
Using the total (or a single) applied force instead of the NET force — if multiple forces act on an object, F = ma only works with their combined, resultant force.
Quick Review
- F = ma — net force equals mass times acceleration.
- Bigger force → bigger acceleration; bigger mass → smaller acceleration (for the same force).
- Always use the NET (resultant) force, not just one of several forces acting.