Kinetic energy is the energy a body has thanks to its motion. The faster and the heavier a body is, the more kinetic energy it possesses. It is a fundamental concept of mechanics, crucial for analysing collisions, braking and work. In this article we discuss the kinetic energy formula and show the calculations using an example.
The kinetic energy formula
We calculate the kinetic energy of a body of mass m moving with a speed v from the formula:
- Ek = ½ × m × v² — kinetic energy equals half the product of the mass and the square of the speed
The symbol Ek stands for kinetic energy, m for mass, and v for the speed of the body.
SI units
In the SI system we measure energy in joules (J):
- Mass m — kilogram (kg)
- Speed v — metre per second (m/s)
- Energy Ek — joule (J), where 1 J = 1 kg·m²/s²
If the speed is given in km/h, first convert it into m/s by dividing by 3.6.
Why is speed so important?
In the formula the speed appears squared, so it has a much greater effect on the energy than the mass. Doubling the mass doubles the kinetic energy, but doubling the speed increases it fourfold. That is why at high speeds the effects of collisions grow so sharply.
Worked example
A car with a mass of m = 1000 kg is travelling at a speed of v = 20 m/s. We calculate its kinetic energy.
- We apply the formula Ek = ½ × m × v².
- First the square of the speed: v² = 20² = 400 m²/s².
- We substitute: Ek = 0.5 × 1000 × 400.
- We calculate: Ek = 0.5 × 400 000 = 200 000 J.
The kinetic energy of the car is 200 000 J, that is 200 kJ. This is the energy that the braking system must dissipate in order to stop the vehicle.
What happens when the speed is doubled?
If the same car were travelling at 40 m/s, its energy would be: Ek = 0.5 × 1000 × 40² = 0.5 × 1000 × 1600 = 800 000 J. The speed has doubled, but the energy has quadrupled. This nicely illustrates the role of the square of the speed in the formula.
Kinetic energy in nature and technology
Kinetic energy is not only a topic for school problems. We come across it wherever something is moving. Water flowing in a river has kinetic energy, which the turbines of hydroelectric power plants convert into electricity. The wind driving the blades of a wind turbine also carries kinetic energy. A bullet, a spun-up washing machine drum, a rolling bicycle or a falling ball — each of these bodies has energy of motion described by the same formula. The greater the mass and speed, the more work such a body can do before it stops.
Kinetic energy and braking work
To stop a moving body, the brakes have to dissipate all of its kinetic energy. According to the principle of conservation of energy, the braking work equals the kinetic energy. That is why the braking distance grows with the square of the speed — at twice the speed a vehicle needs four times the distance to stop.
Second example: speed from the energy of a body
A body with a mass of m = 2 kg has a kinetic energy of Ek = 36 J. We calculate its speed.
- We rearrange the formula: v = the square root of (2 × Ek / m).
- We substitute: v = the square root of (2 × 36 / 2).
- We calculate the inside: 2 × 36 / 2 = 36.
- The square root: v = 6 m/s.
The body is moving at a speed of 6 m/s. This shows that the formula can be rearranged to find the speed.
Most common mistakes
- Not squaring the speed — this is the most serious mistake, understating the result.
- Speed in km/h instead of m/s — always convert the units before substituting.
- Omitting the factor of ½ — kinetic energy is half the product of the mass and the square of the speed.
- Wrong order of operations — first we square the speed, only then do we multiply by the mass.
Frequently asked questions
- How does kinetic energy differ from potential energy? Kinetic energy comes from motion, while potential energy comes from the position of a body, for example its height above the ground.
- Can kinetic energy be negative? No. Mass and the square of the speed are always positive, so kinetic energy is never negative.
- What happens to the energy in a collision? It turns into deformation work, heat and sound, which is why high-speed collisions are so dangerous.
Summary
Kinetic energy Ek = ½mv² depends on the mass and the square of the speed, and we express it in joules. Because the speed appears squared, it has a decisive effect on the value of the energy. Remember to convert the units to SI before calculating.
Calculate the kinetic energy of a body: Kinetic Energy Calculator →