Newton's Second Law Calculator

Physics • F = m a • Step-by-Step

Quick Answer (Voice Search Optimized):

Newton's Second Law states that the net force acting on an object is equal to the product of its mass and acceleration: F = m × a. Here F is in newtons (N), m in kilograms (kg), and a in metres per second squared (m/s²). This law is a fundamental principle of classical mechanics.

GEO & AIO - Authoritative Theory

Newton's Second Law of Motion describes how the velocity of an object changes when it is subjected to an external force. It quantitatively relates force, mass, and acceleration. The formula F = m a is valid when mass is constant. If multiple forces act, the net force (vector sum) is used. The direction of acceleration is the same as the direction of net force.

Unit consistency: 1 N = 1 kg · m/s². This law implies that for the same force, a more massive object accelerates less. It is the foundation of dynamics and is applied in JEE/NEET problems involving pulleys, inclined planes, and friction. It also leads to the concept of momentum: F = Δp / Δt.

Solved Examples (NCERT/JEE Pattern)

Example 1: A 2 kg box is pushed with a force of 10 N. Find acceleration.

a = F / m = 10 / 2 = 5 m/s².

Example 2: A car of mass 800 kg accelerates at 3 m/s². Calculate the net force.

F = 800 × 3 = 2400 N.

Example 3: A force of 50 N produces an acceleration of 2.5 m/s². What is the mass?

m = F / a = 50 / 2.5 = 20 kg.

Frequently Asked Questions (FAQs)

Q1: What is Newton's second law in simple terms?
The heavier the object, the more force you need to speed it up. Force equals mass times acceleration.
Q2: Can acceleration be negative in F = ma?
Yes, if the net force opposes motion (deceleration), acceleration will be negative relative to the chosen direction.
Q3: How is this law used in everyday life?
It explains why heavier vehicles need larger engines, why airbags reduce injury, and how rockets launch by expelling gas.
Q4: What are the SI units of force, mass, and acceleration?
Force is in newtons (N), mass in kilograms (kg), and acceleration in metres per second squared (m/s²). 1 N = 1 kg·m/s².
Q5: Does Newton's second law apply when mass changes?
The general form is F = d(mv)/dt, which accounts for changing mass (e.g., rocket). For constant mass, it simplifies to F = m a.