01Why this matters
The square of speed explains why doubling speed makes much more energy available in a collision or braking process.
02See it
03Understand it
Kinetic energy is energy associated with motion. For ordinary speeds, translational kinetic energy is ½mv².
Mass is measured in kilograms and speed in metres per second. Square the speed, multiply by mass, then halve. Kinetic energy is non-negative and is a scalar. It depends on the reference frame: a passenger at rest relative to a train is moving relative to the track.
04Guided example
Find the kinetic energy of a 2 kg trolley moving at 3 m/s.
- Square the speed: 3² = 9 m²/s².
- Multiply by the mass: 2 × 9 = 18.
- Halve the result: Ek = ½ × 18 = 9 J.
05Try it
06Practise it
07Use it in the real world
At twice the speed, the same object has four times the kinetic energy. Under the same constant braking force, this means four times the braking distance in the idealised model.
Go a little deeper
Net work equals the change in kinetic energy. Rotating objects also have rotational kinetic energy, which this translational formula does not include.
08Quick check
09Summary
Kinetic energy is energy associated with motion. For ordinary speeds, translational kinetic energy is ½mv². Halve the result: Ek = ½ × 18 = 9 J.
Before moving on, explain the worked example in your own words. Use the hint on any question you want to revisit.
10Key idea
Ek = ½mv²
Ek: kinetic energy in J; m: mass in kg; v: speed in m/s.
v = √(2Ek/m), for m > 0
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