Newton's laws of motion, explained with examples
Newton's three laws describe how forces change motion. They explain everything from a car braking to a rocket launching, and they underpin the whole forces topic.
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Newton's first law
If the resultant force on an object is zero, a stationary object stays still, and a moving object keeps moving at the same speed in the same direction.
This surprises many people, because everyday experience suggests moving things slow down on their own. They slow down because of friction and air resistance, which are forces. With no resultant force, as in deep space, an object would carry on forever. The first law also means that a car driving at a steady 30 mph on a straight road has a resultant force of zero: the driving force exactly balances friction and air resistance.
The tendency of an object to stay at rest or keep moving uniformly is called inertia. Objects with more mass have more inertia, so they are harder to start, stop or turn. Separate Physics students learn that inertial mass is a measure of how difficult it is to change an object's velocity, defined as force divided by acceleration.
Newton's second law
The acceleration of an object is proportional to the resultant force on it, and inversely proportional to its mass.
In equation form: F = m a, where F is the resultant force in newtons (N), m is the mass in kilograms (kg) and a is the acceleration in m/s². One newton is the force needed to give a 1 kg mass an acceleration of 1 m/s². A bigger force gives a bigger acceleration; a bigger mass gives a smaller one for the same force.
The key word is resultant. Always add up all the forces, taking direction into account, before using F = ma.
Newton's third law
Whenever two objects interact, the forces they exert on each other are equal in size and opposite in direction.
When you push on a wall, the wall pushes back on you with the same force. When a swimmer pushes water backwards, the water pushes the swimmer forwards. A rocket pushes exhaust gases down, and the gases push the rocket up. The two forces in a pair always act on different objects and are always the same type of force.
A common confusion: a book resting on a table has its weight acting down and the normal contact force acting up. These are equal and opposite, but they are not a third-law pair, because they both act on the book. They balance because of the first law. The third-law partner of the book's weight is the book's gravitational pull on the Earth.
Worked examples
Example 1: resultant force
A boat's engine provides 1500 N forwards. Water resistance is 900 N. Find the resultant force.
- Resultant = 1500 − 900 = 600 N forwards.
Example 2: F = ma
The boat has mass 400 kg. Find its acceleration.
- a = F/m = 600/400 = 1.5 m/s².
Example 3: finding a force
A 1200 kg car accelerates at 2.5 m/s². What resultant force is acting?
- F = ma = 1200 × 2.5 = 3000 N.
Example 4: braking
A 900 kg car slows from 20 m/s to rest in 4 s. Find the braking force.
- a = (0 − 20)/4 = −5 m/s².
- F = 900 × (−5) = −4500 N, a braking force of 4500 N.
Example 5: a lift
A lift of mass 800 kg is pulled up by a cable with tension 9000 N. Find its acceleration. (g = 9.8 N/kg)
- Weight = 800 × 9.8 = 7840 N. Resultant = 9000 − 7840 = 1160 N upwards.
- a = 1160/800 = 1.45 m/s² upwards.
Terminal velocity: all three laws together
When a skydiver jumps, weight is the only significant force, so there is a resultant force downwards and they accelerate (second law). As speed increases, air resistance increases, so the resultant force and the acceleration decrease. Eventually air resistance equals weight, the resultant force is zero, and the skydiver falls at a constant speed: terminal velocity (first law). Opening the parachute suddenly increases air resistance, giving a resultant force upwards, so the skydiver decelerates until a new, lower terminal velocity is reached.
Newton's laws and momentum (Higher)
The second law can also be written as force equals rate of change of momentum: F = mΔv/Δt. This form explains car safety features. Crumple zones, seatbelts and airbags increase the time it takes for a passenger to stop, so the same change in momentum happens over a longer time and the force on the body is smaller.
The acceleration required practical
This practical investigates how acceleration depends on force and on mass. A trolley on a bench is pulled by a string over a pulley attached to hanging masses. Light gates, or a stopwatch and marked distances, measure the acceleration.
- Varying force: move masses from the trolley to the hanger one at a time, so the total mass of the system stays constant while the force changes. Acceleration should be directly proportional to force.
- Varying mass: keep the hanging mass constant and add masses to the trolley. Acceleration should be inversely proportional to mass.
Friction and the timing method are the main sources of error. Tilting the runway slightly to compensate for friction, and using light gates rather than a stopwatch, improve accuracy.
Common mistakes
- Using one force instead of the resultant force in F = ma.
- Thinking a moving object needs a resultant force to keep moving at a constant velocity.
- Calling weight and the normal force a third-law pair.
- Using grams instead of kilograms.
Practice questions
Try each one before opening the answer.
Q1. A 5 kg trolley has a resultant force of 20 N. Find its acceleration.
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Q2. A 60 kg cyclist accelerates at 0.5 m/s². Find the resultant force.
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Q3. A car moves at constant velocity. The driving force is 2000 N. What is the total resistive force?
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Q4. A gun recoils when it fires a bullet. Which law explains this?
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Q5. The same force acts on a 2 kg and a 6 kg mass. How do their accelerations compare?
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Frequently asked questions
Are Newton's laws in Combined Science?
Yes. All three laws are in the forces topic for both Combined Science and separate Physics. Inertial mass is mainly separate Physics, Higher tier.
Do I need to learn F = ma?
Yes. For GCSE exams in 2025, 2026 and 2027, an equations sheet is provided with the Physics and Combined Science papers, including the equations students previously had to recall. Check the arrangements for your exam year, and learn the equation anyway, because using it fluently saves time.
Key takeaways
- First law: zero resultant force means no change in velocity.
- Second law: F = ma, using the resultant force.
- Third law: interaction pairs are equal, opposite, and act on different objects.
- Terminal velocity happens when air resistance balances weight.
- More mass means more inertia.