Work Done and Kinetic Energy

What 'work' really means in physics

In everyday speech, "work" can mean homework, a job, or anything tiring. In physics it has one precise meaning: work is done whenever a force moves something through a distance. Push a trolley across a car park and you do work on it. Lift a box onto a shelf and you do work against gravity. But hold that box perfectly still, and — surprisingly — you do no work at all, because nothing moves.

Work and energy are two sides of the same coin: doing work transfers energy. In this lesson you will meet the two key equations that connect force, distance, and the energy of motion. If you have studied energy, work and power, this lesson focuses in on the link between work and kinetic energy — the energy of moving things.

Work done: W = Fd

Work done is defined as the force applied multiplied by the distance moved in the direction of the force:

W = F × d

where:

• W is the work done in joules (J),
• F is the force in newtons (N),
• d is the distance moved in metres (m).

One joule is the work done when a force of 1 newton moves something 1 metre. So 1 J = 1 N × 1 m. The joule is also the unit of energy — because doing work means transferring energy.

Worked example. A gardener pushes a wheelbarrow with a steady force of 80 N for a distance of 15 m. The work done is:

W = F × d = 80 × 15 = 1200 J

Kinetic energy: KE = ½mv²

A moving object carries energy purely because it is moving — this is kinetic energy. Its formula is:

KE = ½ × m × v²

where:

• KE is the kinetic energy in joules (J),
• m is the mass in kilograms (kg),
• v is the velocity in metres per second (m/s).

The most important feature is the v²: velocity is squared. This means kinetic energy grows extremely fast as speed increases.

Worked example. A 1000 kg car travels at 20 m/s. Its kinetic energy is:

KE = ½ × m × v² = ½ × 1000 × 20² = ½ × 1000 × 400 = 200 000 J (200 kJ)

Now double the speed to 40 m/s:

KE = ½ × 1000 × 40² = ½ × 1000 × 1600 = 800 000 J (800 kJ)

Doubling the speed gave four times the kinetic energy. This is exactly why higher speeds need disproportionately longer braking distances — a key road-safety fact.

The work-energy principle

Here is the idea that ties the two equations together: the work done on an object equals the change in its kinetic energy.

work done = change in kinetic energy

When a force speeds an object up, the work it does becomes extra kinetic energy. When friction or brakes slow an object down, they do negative work, removing kinetic energy and usually turning it into heat. This principle lets you solve problems without ever finding the acceleration.

Worked example. A 1500 kg car moving at 20 m/s brakes to a stop. How much work must the brakes do?

KE at start = ½ × 1500 × 20² = 300 000 J KE at end = 0 J Work done by brakes = change in KE = 300 000 J (turned into heat in the brake discs)

Why this matters

The work-energy link is everywhere. Engineers use it to size the brakes on a train, to design roller-coasters that have just enough energy to clear each hill, and to calculate the safe stopping distance for cars. The v² rule is one reason speed limits exist: a small rise in speed means a large rise in the energy that must be removed to stop. Connecting forces to energy this way is one of the most powerful tools in physics, and it links naturally to Newton's laws of motion.

Try it yourself! 🧪

Show kinetic energy doing work with a rolling ball.

You need a marble or small ball, a ramp (a ruler with a groove or a length of pipe), a flat smooth floor, and a small light object to act as a target (a cardboard "skittle" or a small empty cup).

1. Set up the ramp and place the target a fixed distance from the bottom.
2. Release the ball from halfway up the ramp. Watch how far it knocks the target.
3. Now release it from the top of the ramp, so it reaches the bottom moving faster. The target is knocked much further.
4. The faster ball had more kinetic energy (because of the v² term) and so did more work on the target.

For a tidy comparison, mark how far the target slides each time. You are seeing energy of motion being transferred as work — the same physics that determines how hard any moving object hits. To explore where the ball's energy came from at the top of the ramp, see energy, work and power.