Newton's Second Law Formula

The Formula

F = ma \quad \text{or} \quad a = \frac{F}{m}

When to use: Push harder and you get faster acceleration; heavier object means slower acceleration for the same push.

Quick Example

Same push: empty shopping cart accelerates fast, full cart accelerates slow.

What This Formula Means

The acceleration of an object is equal to the net force applied divided by its mass, in the direction of the force.

Push harder and you get faster acceleration; heavier object means slower acceleration for the same push.

Worked Examples

Example 1

easy
A 10 \text{ kg} cart is pushed with a net force of 50 \text{ N}. What is the acceleration of the cart?

Solution

  1. 1
    Write Newton's second law: F_{\text{net}} = ma, where F_{\text{net}} is net force, m is mass, and a is acceleration.
  2. 2
    Rearrange to solve for acceleration: a = \frac{F_{\text{net}}}{m}
  3. 3
    Substitute the given values: a = \frac{50}{10} = 5 \text{ m/s}^2

Answer

a = 5 \text{ m/s}^2
Newton's second law quantifies the relationship between net force, mass, and acceleration. Greater force produces greater acceleration for the same mass.

Example 2

medium
A 1200 \text{ kg} car accelerates from rest to 20 \text{ m/s} in 8 \text{ seconds}. What net force is required?

Why This Formula Matters

The fundamental equation for predicting motion when forces are known.

Frequently Asked Questions

What is the Newton's Second Law formula?

The acceleration of an object is equal to the net force applied divided by its mass, in the direction of the force.

How do you use the Newton's Second Law formula?

Push harder and you get faster acceleration; heavier object means slower acceleration for the same push.

Why is the Newton's Second Law formula important in Physics?

The fundamental equation for predicting motion when forces are known.

What do students get wrong about Newton's Second Law?

F must be the NET force — the vector sum of all forces, not just one individual push.

What should I learn before the Newton's Second Law formula?

Before studying the Newton's Second Law formula, you should understand: force, mass, acceleration.

← Back to Newton's Second Law See All Examples Practice Problems