10 Newton's second law examples in everyday life (F = ma)

Newton's second law says the resultant force on an object equals its mass times its acceleration: F = ma. You can see it every time you push a shopping trolley. Give an empty trolley and a full one the same push, and the empty one shoots off while the full one barely creeps forward. Same force, more mass, less acceleration.

In this post we work through 10 everyday examples of the law with numbers, see where the newton comes from, work out a car's acceleration step by step, and clear up a mistake that costs a lot of students marks.

This post goes with letsBug Physics, episode 1 (Class 9 science in India, GCSE and IGCSE physics). Watch it, or read on: the post adds more everyday examples and exam-style questions with model answers.

Newton's second law in simple words (formula and units)

A resultant force changes how an object moves: it can speed it up, slow it down or turn it in a new direction. Velocity is speed in a given direction, and acceleration is how quickly velocity changes: the change in velocity each second, measured in metres per second squared (m/s²). The second law tells us how much acceleration a force produces. Isaac Newton published it, in words, in his book the Principia in 1687, more than 300 years ago.

• 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)

You'll often need it rearranged: a = F / m to find the acceleration, and m = F / a to find the mass. "Resultant force" is the GCSE term. The NCERT Class 9 book calls the same thing the net force. Both mean every push and pull on the object added together, taking their directions into account. Some books, including NCERT's, also state the law using momentum: the resultant force equals the rate of change of momentum. For a fixed mass, that's the same as F = ma.

Newton's second law examples in everyday life

The first two examples show the two ideas packed inside a = F / m: the bigger the force, the bigger the acceleration, and the bigger the mass, the smaller the acceleration. The others show that slowing down and turning are accelerations too, why a slower stop means a smaller force, and how the same law runs lifts, jumps, smashes and rockets. Here are all 10 at a glance:

1. Pushing a shopping trolley (more mass, less acceleration)

Say the empty trolley has a mass of 20 kg and the full one 80 kg, and each gets a 40 N push (we'll ignore friction, so 40 N is the resultant force):

• empty trolley: a = 40 / 20 = 2 m/s²
• full trolley: a = 40 / 80 = 0.5 m/s²

Four times the mass gives a quarter of the acceleration. Mass is a measure of inertia: how strongly an object resists a change in its motion. It's the same reason you can pass a basketball with one push, but the same push on a stalled car barely moves it. A bike works the same way: pedal just as hard with a heavy bag on the carrier, and you pull away more slowly.

2. Kicking a football harder (more force, more acceleration)

Tap a football and it rolls away slowly. Kick it hard and it flies. The ball's mass hasn't changed, but the force from your foot has. For the same ball, double the force gives double the acceleration while your foot is pushing on it. Push the 20 kg trolley with 80 N instead of 40 N and its acceleration doubles from 2 m/s² to 4 m/s².

3. Braking a car vs a lorry (slowing down is acceleration too)

When a driver brakes, the resultant force on the car points backwards, so the acceleration points backwards and the car slows down. Say a 1200 kg car brakes with a resultant force of 6000 N: a = 6000 / 1200 = 5 m/s² backwards, so it loses 5 m/s of speed every second. Load the same car with passengers and luggage, and the same braking force gives a smaller deceleration (deceleration just means slowing down), so it takes longer to stop.

Now say a loaded lorry has a mass of 36,000 kg, 30 times the car's. The same 6000 N would give it a = 6000 / 36,000 = about 0.17 m/s², a thirtieth of the car's deceleration. To slow down at 5 m/s² like the car, the lorry needs F = 36,000 × 5 = 180,000 N of braking force, 30 times as much. With less than that, the lorry takes much longer to stop.

4. Going round a corner (changing direction)

A car can go round a bend at a steady 30 km/h and still be accelerating, because its direction is changing. The force that does it is friction between the tyres and the road, pushing the car sideways towards the inside of the bend. Say our 1200 kg car takes a bend with a radius of 20 m at 30 km/h (about 8.33 m/s). The acceleration towards the middle of the bend is a = v² / r (a formula you'll meet later in physics) = 8.33² / 20, about 3.5 m/s². So the road has to push sideways with about F = 1200 × 3.5 = 4200 N. That's why cars skid on ice: with too little friction, there isn't enough sideways force to turn.

5. Catching a cricket ball (pull your hands back)

A fielder pulls their hands back while catching a fast ball. The ball still has to lose all its speed, but it does so over a longer time, so its deceleration is smaller. By F = ma, a smaller deceleration needs a smaller force, so the catch stings less. NCERT's Grade 9 book puts it this way: "Applying a smaller force to the moving ball also minimises injury to the fielder."

Let's put numbers on it. The biggest ball in the MCC Laws of Cricket (Law 4 calls it Size 1) weighs 156 g to 163 g when new, so say 160 g, or 0.16 kg. Say it arrives at 30 m/s (108 km/h).

• Stiff hands, say the ball stops in 0.02 s: a = change in velocity / time = 30 / 0.02 = 1500 m/s², so F = ma = 0.16 × 1500 = 240 N.
• Hands pulled back, say the stop takes 0.1 s: a = 30 / 0.1 = 300 m/s², so F = 0.16 × 300 = 48 N.

Five times the stopping time, a fifth of the force. You can also write the law as force = change in momentum / time. The ball's momentum (mass × velocity) drops by 0.16 × 30 = 4.8 kg m/s either way, and 4.8 / 0.02 = 240 N while 4.8 / 0.1 = 48 N: the same answers.

6. A lift starting up (why you feel heavier)

Stand on bathroom scales in a lift and watch the reading jump as the lift starts to go up. Two forces act on you: your weight pulling down, and the floor pushing up. To accelerate you upwards, the floor has to push up harder than your weight. Say you have a mass of 60 kg (a weight of 60 × 9.8 = 588 N) and the lift speeds up at 1 m/s²:

• resultant force needed: F = ma = 60 × 1 = 60 N upwards
• so the floor pushes up with 588 + 60 = 648 N

Scales measure that push, so they read 648 / 9.8 = about 66.1 kg instead of 60 kg. That bigger push from the floor is the "heavier" feeling. When the lift speeds up going down at 1 m/s², the floor pushes with only 588 − 60 = 528 N, the scales read about 53.9 kg and you feel lighter. At a steady speed the reading is back to 60 kg: no acceleration, balanced forces.

7. Jumping (push the ground, the ground pushes you)

To jump, you push down on the ground with your legs, and the ground pushes back up on you (that pair is Newton's third law). While your legs straighten, the upward push is bigger than your weight. Say a 60 kg jumper gets a push of 1200 N from the ground:

• resultant force = 1200 − 588 = 612 N upwards
• a = F / m = 612 / 60 = 10.2 m/s² upwards

Push harder and the resultant force goes up, so you leave the ground faster and jump higher. Once your feet leave the ground, the only force left is your weight, so you slow down on the way up and fall back.

8. Seatbelts and airbags (a longer stop in a crash)

In a crash, a passenger has to stop with the car. The change in momentum is fixed by the speed, so the only thing safety kit can change is the time. OpenStax Physics says: "The momentum change is the same for an occupant whether an airbag is deployed or not. But the force that brings the occupant to a stop will be much less if it acts over a larger time." Say a 60 kg passenger is moving at 15 m/s (54 km/h), so they lose 60 × 15 = 900 kg m/s of momentum:

• stopped by a hard dashboard, say in 0.01 s: F = 900 / 0.01 = 90,000 N
• stopped by a seatbelt and airbag that stretch and squash, say over 0.1 s: F = 900 / 0.1 = 9000 N

Ten times the stopping time, a tenth of the force. It's the cricket catch again: the seatbelt and airbag are a pair of hands pulling back with you.

9. A badminton smash (a tiny mass, a huge acceleration)

A shuttlecock is very light. The Laws of Badminton say: "The shuttle shall weigh from 4.74 to 5.50 grams." According to Guinness World Records, the fastest badminton hit in competition by a man is 426 km/h, by Mads Pieler Kolding of Denmark in Bangalore in 2017. That's 426 / 3.6 = about 118 m/s.

Say the shuttle has a mass of 5 g (0.005 kg) and starts from rest, to keep the numbers simple, and the strings push on it for 1 millisecond (0.001 s, a round number for illustration):

• a = change in velocity / time = 118 / 0.001 = 118,000 m/s²
• F = ma = 0.005 × 118,000 = 590 N

That's about 12,000 times the 9.8 m/s² of a falling apple, all because the mass is so small. Give a 160 g cricket ball the same 590 N for the same 0.001 s, and it only gains 590 × 0.001 / 0.16 = about 3.7 m/s.

10. A rocket lifting off (thrust minus weight)

A Falcon 9 rocket has a mass of about 549,000 kg at lift-off, and its nine engines give about 7.6 million newtons (7.6 MN) of thrust at sea level. Its weight is 549,000 × 9.8 = about 5.4 MN downwards.

• resultant force = 7.6 MN − 5.4 MN = about 2.2 MN upwards
• a = F / m = 2,200,000 / 549,000 = about 4 m/s² upwards

Resultant force first, just like the car below. And as the engines burn fuel, the rocket's mass goes down, so the same thrust would give a bigger and bigger acceleration. We work through why the push from the exhaust works with no air in how rockets work in space.

What is one newton?

The unit of force is defined by this law. One newton is the force that gives a mass of 1 kg an acceleration of 1 m/s². So:

That's also why F = ma has no extra number in it: the newton was chosen to make the numbers line up exactly. To feel what 1 N is like, rest a small apple of about 100 g on your palm. Your hand pushes up on it with about 1 N, enough to balance its weight (W = mg = 0.1 kg × 9.8 N/kg = 0.98 N).

How to find the resultant force with a free-body diagram

Real objects usually have several forces on them at once. To handle that, draw a free-body diagram: the object as a simple box, with an arrow for every force acting on it. Each arrow points the way the force acts, and its length shows how big it is.

• Forces in the same direction add.
• Forces in opposite directions subtract.
• For a car on a flat road, the weight (down) and the road's push (up) cancel, so you only need the forwards and backwards forces.

Whatever is left over is the resultant force. That's the F that goes into F = ma.

Worked example: how fast does a car speed up?

A car has a mass of 1200 kg. Its engine gives a driving force of 3000 N, and friction plus air resistance push back with 600 N. What is its acceleration?

1. Resultant force: 3000 N − 600 N = 2400 N forwards.
2. Acceleration: a = F / m = 2400 N / 1200 kg = 2 m/s² forwards.
3. What it means: every second, the car gains 2 m/s of speed. Starting from rest, it's doing 2 m/s after 1 s, 4 m/s after 2 s and 6 m/s after 3 s, as long as the forces stay the same. In real life air resistance grows as the car speeds up, so the acceleration gets smaller.

Do moving things need a force to keep moving?

It feels true. Stop pedalling your bike and you slow down. But you slow down because friction and air resistance are still pushing backwards on you, not because a force has been "used up". Take those away and nothing slows you.

An air hockey table shows it. With the air off, the puck slides a short way and stops. With the air on, there's almost no friction, and the puck glides along with hardly any change in speed. A force isn't needed to keep something moving. A resultant force is only needed to change its motion.

Why does constant velocity mean balanced forces?

So what about a car cruising along a straight motorway at a steady speed? The engine is still pushing, but as the car sped up, air resistance grew until the resistive forces exactly balanced the driving force. The resultant force is zero, so a = 0 / m = 0, and the velocity stays the same. A skydiver at terminal velocity is the same: air resistance grows as they speed up until it equals their weight, and then they fall at a steady speed.

That's Newton's first law: with no resultant force, an object stays at rest or keeps moving at a constant velocity. You can think of the first law as the second law with F = 0.

Exam-style questions with model answers

Q1 (2 marks). Calculate the resultant force needed to accelerate a 70 kg sprinter at 3 m/s².

Q2 (3 marks). An 800 kg car has a driving force of 2500 N. The resistive forces on it are 500 N. Calculate its acceleration.

Q3 (2 marks). A resultant force of 12 N gives a trolley an acceleration of 4 m/s². Calculate the mass of the trolley.

Q4 (3 marks). A resultant force of 20 N acts on a 500 g trolley. Calculate its acceleration.

Q5 (2 marks). A car moves along a straight, flat road at a constant speed. Its driving force is 1500 N. State the size of the resistive forces on it, and explain your answer.

Keep going

• Watch the full lesson on Newton's second law, F = ma.
• Next in the series: how rockets work in space with no air, which is Newton's third law, with F = ma used on a real Falcon 9.
• Speed vs velocity, and why a full lap has zero displacement: distance vs displacement.
• Another letsBug physics explainer: how GPS works without internet, and why it needs Einstein.

Checked on 20 October 2026 against the 12 sources below.

Sources

• OpenStax Physics: 4.3 Newton's second law of motion (F = ma, a proportional to F and to 1/m, 1 N = 1 kg m/s², the basketball and the stalled car)
• OpenStax Physics: 4.2 Newton's first law of motion: inertia (the air hockey puck, inertia)
• NCERT, Exploration, Science for Grade 9: Chapter 6, How Forces Affect Motion (net force, the definition of the newton, 100 g in your palm is about 1 N, momentum form, catching a cricket ball, airbags and seat belts)
• OpenStax Physics: 8.1 Linear momentum, force, and impulse (airbags and a longer stopping time)
• MCC Laws of Cricket: Law 4, the ball (a Size 1 ball weighs 156 g to 163 g when new)
• BWF: Laws of Badminton, Law 2.2.6 (a shuttle weighs 4.74 g to 5.50 g)
• Guinness World Records: Fastest badminton hit in competition (male) (426 km/h, 2017)
• NASA Glenn Research Center: Newton's laws of motion
• Wikipedia: Newton's laws of motion (the Principia, 1687), Newton (unit) and Falcon 9 (549,000 kg, 7,607 kN at sea level, 9 engines)
• Try it yourself: PhET's free Forces and Motion: Basics simulation

Every fact in this post was checked against these sources. Numbers that start with "say" (the trolleys, cars, lorry, people, speeds and stopping times) are round example numbers chosen to keep the arithmetic simple; the ball, shuttle, smash speed and Falcon 9 figures are real. All the arithmetic was run in Python before publishing.