Why does the same force accelerate a light object more than a heavy one?

Rearranging F = ma gives a = F ÷ m. For a fixed force, a larger mass m makes the acceleration a smaller. This is why an empty shopping trolley speeds up far more easily than a fully loaded one under the same push — mass resists changes in motion, a property called inertia.

Is F = ma the same as weight = mass × gravity?

They are the same equation in a special case. Weight is the force of gravity on a mass, so W = mg is just F = ma with the acceleration being g, the acceleration due to gravity (about 9.8 m/s²). So weight is a particular example of Newton's second law.

Force, Mass and Acceleration (F = ma) | Physics

The equation that links forces and motion

Push a shopping trolley and it speeds up. Push harder and it speeds up faster. Load it with bricks and the same push barely moves it. Hidden inside these everyday experiences is one of the most important equations in all of physics — Newton's second law, F = ma. It ties together three ideas you may already know separately: force, mass, and acceleration.

If you have met Newton's laws of motion in overview, this lesson digs deeper into the second law and shows you how to actually calculate with it.

Stating Newton's second law

Newton's second law says:

The resultant force on an object equals its mass multiplied by its acceleration. F = m × a

where:

F is the resultant force in newtons (N),
m is the mass in kilograms (kg),
a is the acceleration in metres per second squared (m/s²).

The word resultant is crucial. Objects often have several forces on them at once — a push, friction, gravity, air resistance. The resultant force is the single force left after you combine them all. It is this net force, not any individual push, that determines the acceleration.

What is a newton?

The unit of force, the newton (N), is defined directly from this equation. One newton is the resultant force needed to give a mass of 1 kilogram an acceleration of 1 m/s². In other words, 1 N = 1 kg × 1 m/s². This neat definition is why the equation works so cleanly in SI units — no awkward conversion factors are needed.

Rearranging the formula

Like the speed formula, F = ma can be rearranged to find whichever quantity you need:

To find force: F = m × a
To find mass: m = F ÷ a
To find acceleration: a = F ÷ m

A formula triangle helps: put F on top with m and a underneath. Cover the quantity you want, and the triangle shows the calculation.

Worked examples

Example 1 — finding force. A 1200 kg car accelerates at 2.5 m/s². What resultant force does the engine and road provide?

F = m × a = 1200 × 2.5 = 3000 N

Example 2 — finding acceleration. A resultant force of 90 N acts on a 30 kg go-kart. What is its acceleration?

a = F ÷ m = 90 ÷ 30 = 3 m/s²

Example 3 — combining forces first. A 50 kg sled is pushed with a force of 200 N forwards, while friction pushes back with 50 N. Find the acceleration.

First find the resultant force: 200 − 50 = 150 N forwards. Then a = F ÷ m = 150 ÷ 50 = 3 m/s²

Notice you must work out the resultant force before using F = ma. Forgetting friction is one of the most common mistakes.

Why mass resists motion

Rearranged as a = F ÷ m, the equation reveals something deep: for a fixed force, a bigger mass gives a smaller acceleration. Mass is a measure of an object's inertia — its resistance to changes in motion. This is why a loaded lorry needs a far bigger force to speed up or stop than a bicycle. The same idea explains why heavy objects are hard to start and hard to stop. You can explore the difference between mass and weight in weight vs mass.

Weight as a special case

Weight is simply the force of gravity on a mass. Because gravity gives every falling object the same acceleration g (about 9.8 m/s²), the weight of an object is:

Weight = mass × g, or W = mg

This is just F = ma with the acceleration being g. So weight is not a separate idea — it is Newton's second law applied to gravity.

Why this matters

F = ma is the workhorse of mechanics. Rocket engineers use it to calculate the thrust needed to lift a spacecraft; car designers use it to predict crash forces and design crumple zones; even animators use it to make falling objects look realistic. Almost any problem about why things move the way they do comes back to this one short equation.

Try it yourself! 🧪

See how force and mass change acceleration.

You need a smooth table, a small toy car or trolley, some string, a pulley or the rounded edge of the table, a small bucket or cup, and some identical small weights (coins work).

Tie string to the car, run it over the table edge, and hang the cup off the end so gravity on the cup pulls the car along.
Add one coin to the cup and time how long the car takes to travel a fixed distance. The pull of gravity on the coin is the driving force.
Add more coins (more force) and repeat. The car accelerates faster each time — more force, more acceleration.
Now keep the force the same but add mass to the car (tape coins on top). It accelerates more slowly — more mass, less acceleration.

You have demonstrated both halves of F = ma: acceleration grows with force and shrinks with mass. Keep your hands and feet clear of the falling cup, and use light weights so nothing drops hard.

Force, Mass and Acceleration (F = ma)

Key takeaways