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Work–energy theorem
Beginner
Net work equals the change in kinetic energy.
W_net = ΔKThe net work on a body equals its change in kinetic energy, W_net = K_f − K_i. It gives speeds without solving for time or acceleration.
A 2 kg block pushed 5 m by a net 8 N from rest: ½·2·v² = 40, v = 6.3 m/s.
Use the net work, including friction and gravity.
In more detail
The work-energy theorem states that the net work done on an object equals its change in kinetic energy. It is a powerful way to find speeds without solving for acceleration.
Real-world uses
- Estimating the speed of a car after braking over a known distance.
- Calculating how fast a roller coaster is moving at the bottom of a drop.
- A cyclist braking on a hill uses the work-energy theorem to find how much the brakes must remove in kinetic energy.
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Frequently asked questions
Does the theorem require constant force?
No. It holds for any net work, including variable forces.
How is it different from F = ma?
It gives the change in speed directly, without needing the acceleration at each moment.
Does the work-energy theorem include friction?
Yes, if you include friction's work in the net work. Friction does negative work and reduces the kinetic energy.
Related topics in Work, Energy & Power
Work done by a variable force · Work done by a spring · Kinetic energy · Potential energy · Gravitational potential energy · Elastic potential energy