K = ½ m v²

The idea

An object of mass m moving with velocity v has kinetic energy K = (1/2) mv², measured in joules; kinetic energy has no direction.

A faster vehicle

A scooter moves at a certain speed. Then it moves twice as fast.

How do you think its kinetic energy changes when its velocity doubles?

• It becomes 4 times as much
• It becomes 2 times as much
• It stays the same

Mass and velocity

Set the mass and the velocity of the block.

Velocity counts twice

The velocity is squared. When it doubled from 3 to 6 m s⁻¹, the kinetic energy grew from 9 J to 36 J, which is 4 times as much. The mass counts once. Kinetic energy has a size and a unit, but no direction.

An object of mass m moving with velocity v has kinetic energy K = (1/2) m v², measured in joules. Kinetic energy has no direction.

Notes

K = (1/2) m v², in joules. Kinetic energy has no direction; doubling the velocity makes it 4 times as much.

Check yourself

A 4 kg object moves with a velocity of 5 m s⁻¹. What is its kinetic energy, in J?

Answer: 50 J

K = (1/2) × 4 kg × (5 m s⁻¹)² = 50 J.

A cricket ball of mass 0.2 kg is bowled at 43 m s⁻¹. What is its kinetic energy, in J? Give the answer to one decimal place.

Answer: 184.9 J

K = (1/2) × 0.2 kg × (43 m s⁻¹)² = 184.9 J.

The velocity of a vehicle doubles. Its kinetic energy becomes…

Which statement about kinetic energy is correct?

• 2 times the original value. Velocity is squared in K = (1/2) m v². Doubling v gives (2v)² = 4v².
• the same. Kinetic energy depends on the velocity, and (2v)² is 4 times v².
• 4 times the original value — correct. Yes!
• It is measured in joules and has no direction — correct. Yes!
• It points in the direction of the velocity. Kinetic energy has no direction. It is measured in joules.
• It is measured in newtons. Newtons measure force. Kinetic energy is measured in joules.