Kinetic energy, explained with examples

By The STEM-Tutor team · Updated October 2026

Kinetic energy is the energy an object has because it is moving. It explains why speeding is so dangerous, how roller coasters work and where the energy goes when a car brakes.

The equation

E_k = ½ m v²

• E_k is kinetic energy, in joules (J);
• m is mass, in kilograms (kg);
• v is speed, in metres per second (m/s).

Only the speed is squared, not the mass and not the half. Kinetic energy is never negative, because v² is always positive, and it does not depend on direction: a car moving north at 20 m/s has the same kinetic energy as one moving south at 20 m/s.

Why speed matters so much

Because speed is squared, doubling the speed multiplies the kinetic energy by four, and tripling it multiplies it by nine. Doubling the mass only doubles the kinetic energy. This is why small increases in driving speed have big effects on braking distances and on the damage done in a crash. A car at 40 mph has about four times the kinetic energy of the same car at 20 mph, so the brakes must do about four times as much work to stop it.

Worked examples

Example 1: calculating kinetic energy

Find the kinetic energy of a 1200 kg car travelling at 20 m/s.

• E_k = ½ × 1200 × 20² = 600 × 400.
• E_k = 240,000 J, or 240 kJ.

Example 2: grams

A 150 g ball is thrown at 12 m/s. Find its kinetic energy.

• m = 0.15 kg. E_k = ½ × 0.15 × 144.
• E_k = 10.8 J.

Example 3: finding speed

A 2 kg trolley has 36 J of kinetic energy. Find its speed.

• Rearrange: v² = 2E_k/m = 72/2 = 36.
• v = 6 m/s. Remember to take the square root at the end.

Example 4: finding mass

A cyclist moving at 8 m/s has 2560 J of kinetic energy. Find the combined mass of the cyclist and bike.

• m = 2E_k/v² = 5120/64.
• m = 80 kg.

Example 5: change in kinetic energy

A 1000 kg car speeds up from 10 m/s to 20 m/s. How much does its kinetic energy increase?

• Before: ½ × 1000 × 100 = 50,000 J. After: ½ × 1000 × 400 = 200,000 J.
• Increase = 150,000 J. You cannot use the change in speed (10 m/s) in the formula; find both energies and subtract.

Kinetic energy and gravitational potential energy

When an object falls, energy moves from its gravitational potential energy store to its kinetic energy store. If air resistance is small enough to ignore:

loss of GPE = gain in KE, so mgh = ½mv²

The mass cancels, giving v = √(2gh). Every object dropped from the same height lands at the same speed, if air resistance is ignored.

Example 6: a falling object

A ball is dropped from 5 m. Find its speed just before it hits the ground. (g = 9.8 N/kg)

• v = √(2 × 9.8 × 5) = √98.
• v ≈ 9.9 m/s.

Example 7: a roller coaster

A 500 kg roller coaster car starts from rest at the top of a 20 m drop. Find its speed at the bottom, ignoring friction. (g = 9.8 N/kg)

• GPE lost = 500 × 9.8 × 20 = 98,000 J = KE gained.
• v² = 2 × 98,000/500 = 392, so v ≈ 19.8 m/s.

Work done and braking

To stop a moving object, a force must do work against its motion: work done = force × distance. When a car brakes, the work done by the friction between the brake pads and discs equals the kinetic energy lost, which is transferred to the thermal energy store of the brakes, making them hot.

Example 8: braking distance

A 1200 kg car at 20 m/s brakes with a constant force of 6000 N. How far does it travel before stopping?

• Kinetic energy = 240,000 J (Example 1). Work done by brakes = F × d.
• 6000 × d = 240,000, so d = 40 m.
• At double the speed, the kinetic energy and so the braking distance would be four times larger: 160 m.

Kinetic energy and momentum compared

Students often mix up kinetic energy and momentum, because both depend on mass and speed. They are different quantities:

• Momentum, p = mv, is a vector with a direction, measured in kg m/s. It is always conserved in a collision when no external forces act.
• Kinetic energy, E_k = ½mv², is a scalar with no direction, measured in joules. In most real collisions, some of it is transferred to heating and sound, so the kinetic energy afterwards is less than before.

Because kinetic energy depends on v², a light, fast object can have more kinetic energy than a heavy, slow one with the same momentum. That is why a bullet does so much damage despite its small mass: it carries a large amount of energy that must be transferred when it stops.

Where kinetic energy goes

Energy is never destroyed, but kinetic energy is often transferred in ways that are not useful. A bouncing ball loses some energy as sound and heating with every bounce, so it rises a little less each time. Air resistance transfers kinetic energy to the thermal store of the surroundings. In exam answers, name the store the energy leaves, the store it enters and the pathway, such as “kinetic energy is transferred to the thermal energy store of the brakes by friction”.

Common mistakes

• Squaring the whole of mv, or forgetting to square v.
• Leaving mass in grams.
• Forgetting the square root when finding speed.
• Using the change in speed in the formula instead of calculating each kinetic energy.

Practice questions

Try each one before opening the answer.

Frequently asked questions

Is E_k = ½mv² on the GCSE equation sheet?

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.

Is kinetic energy in Combined Science?

Yes. Kinetic energy and energy transfers are in the energy topic for both Combined Science and separate Physics.

Key takeaways

• E_k = ½mv², with m in kg and v in m/s.
• Doubling speed quadruples kinetic energy.
• Falling: mgh = ½mv², so v = √(2gh).
• Braking: force × distance = kinetic energy lost.
• Name the stores and pathways when describing transfers.

Related guides

• GCSE Physics energy
• Momentum
• Hooke's law