Newton's Second Law
Newton's second law of motion states that force equals mass times acceleration (F = ma).
Learn how to calculate force, mass, or acceleration with worked examples.
The Formula
F = ma
Force equals mass multiplied by acceleration. This is one of the most fundamental equations in physics.
Variables
| Symbol | Meaning |
|---|---|
| F | Force (measured in newtons, N) |
| m | Mass of the object (measured in kilograms, kg) |
| a | Acceleration (measured in meters per second squared, m/s²) |
Example 1
A 12 kg box is pushed across a floor with an acceleration of 3 m/s². What force is applied?
Identify the values: m = 12 kg, a = 3 m/s²
Apply the formula: F = ma = 12 × 3
F = 36 N
Example 2
A 1,500 kg car accelerates from rest to 20 m/s in 10 seconds. What is the net force?
First find acceleration: a = (v - u) / t = (20 - 0) / 10 = 2 m/s²
Apply the formula: F = ma = 1,500 × 2
F = 3,000 N
When to Use It
Use Newton's second law whenever you need to relate force, mass, and acceleration.
- Calculating the force needed to accelerate an object
- Finding the acceleration produced by a known force
- Determining the mass of an object from force and acceleration measurements
- Solving problems involving friction, tension, or applied forces