Forces change motion, they do not maintain it
Resultant force — The single force that has the same effect as all the forces acting on a body combined.
The hardest idea in mechanics is also the first one: a moving object does not need a force to keep moving. Everyday experience suggests otherwise, because everything we push eventually stops — but it stops because of friction, not because the push ran out.
Newton's first law states that an object stays at rest, or continues at constant velocity in a straight line, unless a resultant force acts on it. Constant velocity and rest are the same case as far as the physics is concerned: both mean no resultant force.
So a force is not what keeps a body moving. A force is what changes how it moves — speeding it up, slowing it down, or bending its path. A spacecraft coasting between planets has no engine running and does not slow down at all.
Constant velocity means balanced forces
A car travelling at a steady 80 km/h has zero resultant force on it. The engine's driving force exactly balances air resistance and friction. Students often write that the driving force must be bigger — it is not, or the car would be accelerating.
Newton's second law
When there is a resultant force, the body accelerates. Newton's second law says the acceleration is proportional to the resultant force and inversely proportional to the mass, which gives the single most used equation in mechanics.
Two things about it are worth stating carefully. The F is the resultant force, not any one of the individual forces — you must combine them first. And the acceleration is always in the same direction as that resultant force.
The inverse relationship with mass is the part that feels intuitive: push a shopping trolley and an identical push produces far less acceleration when it is full. Mass is the measure of that resistance to being accelerated, which is why it is also called inertia.
- F
- resultant forceN
- m
- masskg
- a
- accelerationm s⁻²
A 1200 kg car has a driving force of 3600 N. Air resistance and friction together total 1200 N. Calculate its acceleration, and then the resistive force when it travels at constant speed.
- Resultant force
= 3600 − 1200 = 2400 N.Combine the forces before using F = ma — this is the step most often skipped. a = F/m = 2400 / 1200.a = 2.0 m s⁻².- At constant speed the acceleration is zero, so the resultant force is zero.Newton's first law.
- Therefore resistance
= 3600 N, equal and opposite to the driving force.Not zero — the forces balance, they do not vanish.
a = 2.0 m s⁻²; resistance = 3600 N at constant speed
Newton's third law, and the pair that never cancels
For every force there is an equal and opposite force. If you push a wall with 50 N, the wall pushes you back with 50 N. The two forces are always the same size, always opposite in direction, and always the same type of force.
The point that decides most exam questions is this: the two forces of a third-law pair act on different bodies. They can therefore never cancel each other out, because cancelling only happens between forces acting on the same object.
A book resting on a table makes the distinction clear. The book's weight (Earth pulling book) pairs with the book pulling the Earth up — not with the table's push on the book. The table's push happens to be equal and opposite to the weight, but that is a balance, not a third-law pair.
| Balanced forces | Third-law pair | |
|---|---|---|
| Act on | the same body | two different bodies |
| Type of force | may be different types | always the same type |
| Can they cancel? | yes — that is the point | never |
| Example | weight and table push on a book | Earth pulls book, book pulls Earth |
Friction, drag and terminal velocity
Friction opposes motion between surfaces in contact, and drag does the same job in a fluid. Both convert kinetic energy into internal energy, which is why brakes get hot.
Drag differs from ordinary friction in one crucial way: it increases with speed. That single fact produces terminal velocity, which is one of the most commonly examined sequences in the whole subject.
A skydiver leaving an aircraft has weight acting down and almost no drag, so the resultant force is large and the acceleration is close to g. As speed builds, drag grows. The resultant force shrinks, so the acceleration falls — the diver is still speeding up, but less quickly. Eventually drag equals weight, the resultant force is zero, and the speed stops changing. That constant speed is the terminal velocity.
Opening a parachute increases the drag sharply. Drag now exceeds weight, so the resultant force acts upward and the diver decelerates — slowing down until drag has fallen back to equal weight, giving a new, much lower terminal velocity.
The amber arrow stays the same length for the whole flight — with no horizontal force there is no horizontal acceleration. The cyan arrow shrinks, reverses and grows, because gravity acts on the vertical motion alone.
Key points
- Drag increases with speed; friction between solid surfaces does not.
- Terminal velocity is reached when drag equals weight, giving zero resultant force.
- At terminal velocity the object is still moving fast — it has simply stopped accelerating.
- Opening a parachute makes drag exceed weight, so the diver slows down.
- The new terminal velocity is lower, but it is still reached the same way.
Circular motion
An object moving in a circle at constant speed is still accelerating, and this catches almost everyone out. Velocity is a vector, so it has direction as well as size. Going round a bend changes the direction continuously, so the velocity is changing continuously, and a changing velocity is an acceleration.
That acceleration needs a resultant force, directed towards the centre of the circle. It is called the centripetal force, and it is not a new kind of force — it is whatever real force happens to be doing the job. For a car on a bend it is friction between tyres and road. For a planet it is gravity. For a bucket swung on a rope it is tension.
The force needed grows with speed and with mass, and falls as the radius increases. This is why a car takes a tight bend more slowly than a gentle one: the friction available is fixed, so the speed must come down.
There is no outward force
The feeling of being thrown outwards in a turning car is your body continuing in a straight line while the car turns beneath you — Newton's first law, not a force. Writing "centrifugal force" in an exam answer loses marks. The only force is inward.