Newton's Second Law — F = ma

Newton's second law F = ma explained in plain language: net force, mass and acceleration, key assumptions, and a worked example.

What it means

The equation says acceleration is caused by unbalanced force and resisted by mass. Double the net push and the acceleration doubles; double the mass and the same push produces half the acceleration. Because force and acceleration are vectors, F = ma is really three equations in one — the acceleration always points along the net force, which is not necessarily the direction the object is already moving. The law also defines the newton: one newton is the net force that gives a one-kilogram mass an acceleration of one meter per second squared.

Variables

Assumptions

• F is the net (vector-sum) force, not one individual push or pull
• Mass stays constant while the force acts
• Speeds are far below the speed of light (non-relativistic)
• Measured in an inertial reference frame

Derivation

Newton framed the law as force equaling the rate of change of momentum: $F = dp/dt$. When mass is constant, $p = mv$, so $dp/dt = m(dv/dt) = ma$. The familiar F = ma is the constant-mass special case of the deeper momentum form.

Worked example

Given:

• m = 1200 kg
• a = 2.5 m/s²

1. Write the law: $F = ma$

2. Substitute the values: $F = 1200 \times 2.5$

3. Multiply: $F = 3000\ \mathrm{N}$