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Mechanics
Mechanics

Work-Energy Theorem

Wnet=ΔKE=12mvf2−12mvi2W_{net} = \Delta KE = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2

Net work equals the change in kinetic energy.

Variables

W_net
Net work
Total work done
J
ΔKE
Change in KE
Final minus initial KE
J
m
Mass
Object mass
kg
v_f
Final velocity
Final speed
m/s
v_i
Initial velocity
Initial speed
m/s

Derivation

Integrate F = ma over displacement.

Your notes

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Common questions

What is the Work-Energy Theorem formula?

Work-Energy Theorem is written Wₙₑₜ = ΔKE = 1/2mv_f² - 1/2mvᵢ². Net work equals the change in kinetic energy. It belongs to Mechanics, under Work & Energy.

What are the units in Wₙₑₜ = ΔKE = 1/2mv_f² - 1/2mvᵢ²?

In SI units, W_net is net work, measured in kg·m²/s²; ΔKE is change in ke, measured in kg·m²/s²; m is mass, measured in kg; v_f is final velocity, measured in m/s; v_i is initial velocity, measured in m/s.

How is the Work-Energy Theorem formula derived?

Integrate F = ma over displacement. The result is Wₙₑₜ = ΔKE = 1/2mv_f² - 1/2mvᵢ².