Newton's Second Law Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Newton's Second Law.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass, with the acceleration pointing.

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

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Force, mass, and acceleration are mathematically linked — knowing two gives you the third.

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

Sense of Study hint: When applying Newton's second law, first draw a free-body diagram and identify all forces on the object. Then sum the forces along each axis to find the net force. Finally, use a = F_{\text{net}} / m to find acceleration, or rearrange to find the unknown force or mass.

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?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

hard
A 5 \text{ kg} block on a frictionless surface is pulled by a 30 \text{ N} force at an angle of 30° above the horizontal. What is the horizontal acceleration?

Example 2

medium
A 1500 \text{ kg} truck accelerates at 1.2 \text{ m/s}^2 while resistive forces total 300 \text{ N} opposite the motion. What forward force must the engine provide?
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Background Knowledge

These ideas may be useful before you work through the harder examples.

forcemassacceleration