Kinetic Energy

Definition of Kinetic Energy

Kinetic energy is the energy an object has because it is moving. Any object that is moving has kinetic energy. The amount of kinetic energy depends on two things:

• the mass of the object (how much matter it contains)
• the speed at which the object is moving

The faster an object moves, or the heavier it is, the more kinetic energy it has.

Kinetic Energy Formula

The kinetic energy (KE) of an object can be calculated using the formula:

$$\text{KE} = \frac{1}{2} \times m \times v^2$$

• KE is kinetic energy measured in joules (J)
• m is the mass of the object in kilograms (kg)
• v is the speed of the object in metres per second (m/s)

This formula shows that kinetic energy increases with the square of the speed, meaning if the speed doubles, the kinetic energy increases by four times.

For instance, if a car of mass 1000 kg is moving at 10 m/s, its kinetic energy is:

$$\text{KE} = \frac{1}{2} \times 1000 \times 10^2 = 0.5 \times 1000 \times 100 = 50,000 \text{ J}$$

Energy Transfer Involving Kinetic Energy

Kinetic energy can be transferred to or from other forms of energy. For example:

• A falling object converts gravitational potential energy into kinetic energy as it speeds up.
• A vehicle braking converts kinetic energy into thermal energy due to friction in the brakes.

These energy transfers show how kinetic energy is involved in many everyday processes.

Factors Affecting Kinetic Energy

Two main factors affect the kinetic energy of an object:

• Mass: Increasing the mass increases kinetic energy proportionally. If the mass doubles, kinetic energy doubles.
• Speed: Increasing the speed increases kinetic energy by the square of the speed. For example, doubling the speed increases kinetic energy by four times.

This means speed has a much greater effect on kinetic energy than mass.

For example, a cyclist with a mass of 70 kg moving at 5 m/s has kinetic energy:

$$\text{KE} = \frac{1}{2} \times 70 \times 5^2 = 0.5 \times 70 \times 25 = 875 \text{ J}$$

If the cyclist doubles their speed to 10 m/s, the kinetic energy becomes:

$$\text{KE} = \frac{1}{2} \times 70 \times 10^2 = 0.5 \times 70 \times 100 = 3500 \text{ J}$$

This is four times greater, showing the quadratic effect of speed on kinetic energy.

Quick calculation example: Calculate the kinetic energy of a 2 kg ball moving at 3 m/s.

Using the formula, $\text{KE} = \frac{1}{2} \times 2 \times 3^2 = 0.5 \times 2 \times 9 = 9 \text{ J}$.