Newton's Second Law
When a net force pushes on an object, the object accelerates — it speeds up, slows down, or changes direction. The bigger the force, the bigger the acceleration; the more massive the object, the smaller the acceleration.
The formula
F = m · a
- F — force (N): the net push or pull acting on the object
- m — mass (kg): how much matter the object has — its resistance to being accelerated
- a — acceleration (m/s²): how quickly the object's velocity changes each second
Worked example
A 2 kg cart on a frictionless floor is pushed with a steady 8 N force. How quickly does it speed up?
- m = 2 kg
- F = 8 N
- a = F / m
- a = 8 N / 2 kg
a = 4 m/s²
Test yourself
The same 8 N push now acts on a heavier 4 kg cart. What is its acceleration?
- 4 m/s²
- Correct answer: 2 m/s²
- 32 m/s²
Right! Doubling the mass halves the acceleration: 8 N ÷ 4 kg = 2 m/s².
To give the original 2 kg cart twice the acceleration (8 m/s²), the force must be…
- Correct answer: 16 N
- 4 N
- 8 N
Exactly — acceleration is proportional to force: F = 2 kg × 8 m/s² = 16 N.
Where you see this
A shopping cart is easy to push when empty and hard to push when loaded with groceries — same force, less acceleration, because the mass increased. A car's engine feels weaker hauling a trailer for the same reason: the net force stays similar, but the combined mass is much larger.
Common mistakes
A common misconception is that force is needed to keep something moving at constant velocity — a force is needed only to change velocity, and an object in motion with zero net force keeps moving at the same speed forever. Another is treating F = ma as "force causes velocity" rather than "force causes acceleration" — a large force on a large mass can still produce a tiny acceleration.
How it connects
This builds directly on free fall and projectile motion, where gravity was already accelerating objects — Newton's second law explains that acceleration as F = ma, with F being the object's weight. It leads into conservation of momentum, which is really Newton's second and third laws applied to two objects pushing on each other at once.