Kinetic energy

Kinetic energy is the energy which makes objects move or vibrate.

Calculating kinetic energy

If we know the:

• mass of the object, in kilograms, kg
• speed of the object, in metres per second, m/s

…then we can calculate the amount of kinetic energy it has!

The formula we use is:

\text{Kinetic energy} = \frac{1}{2} \times \text{mass} \times \text{speed}^2

If we put it into symbols, we get:

E_k = \frac{1}{2}mv^2

Where:

• E_k is the kinetic energy, 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

Examples

A car has a mass of 1000 kg and is moving at a speed of 20 m/s. What is its kinetic energy?

• m = 1000\,kg
• v = 20\,m/s
• E_k = \frac{1}{2}mv^2
• E_k = \frac{1}{2} \times 1000\,kg \times (20\,m/s)^2
• E_k = 200,000\,J

A cyclist has a kinetic energy of 1400 J and is moving at a speed of 7 m/s. What is the mass of the cyclist?

• E_k = 1400\,J
• v = 7\,m/s
• E_k = \frac{1}{2}mv^2
• m = \frac{2E_k}{v^2}
• m = \frac{2 \times 1400\,J}{(7\,m/s)^2}
• m = 57.14\,kg

A ball has a kinetic energy of 50 J and a mass of 0.5 kg. What is the speed of the ball?

• E_k = 50\,J
• m = 0.5\,kg
• E_k = \frac{1}{2}mv^2
• v = \sqrt{\frac{2E_k}{m}}
• v = \sqrt{\frac{2 \times 50\,J}{0.5\,kg}}
• v = 14.14\,m/s

flashcards