How Do You Calculate Power (Rate of Work Done)?

• French B
• Geography
• German A
• German A Lit
• German ab initio
• German B
• Global Politics
• History
• History (First Exam 2028)
• Mathematics Analysis and Approaches (AA)
• Mathematics Applications & Interpretation (AI)

• Philosophy
• Physics
• Psychology
• Psychology (First Exam 2027)
• Spanish A
• Spanish A Lit
• Spanish ab initio
• Spanish B
• Sports, exercise and health science (SEHS)
• Theory of Knowledge (TOK)
• World Religions

• MYP English Lang & Lit
• MYP Extended Mathematics
• MYP History

• MYP Individuals & Societies
• MYP Integrated Sciences
• MYP Physics

• MYP Standard Mathematics

The Reasoning and Mechanism

This is part of IB Physics A.3 Work, energy and power, studied by both SL and HL students. Work is an energy transfer, so power measures how quickly that transfer occurs.

For average power:

For a constant force acting in the direction of motion, power can also be calculated using:

More generally, only the component of force parallel to the velocity transfers energy, so $P=Fv\cos\theta$, where $\theta$ is the angle between the force and velocity.

The second equation follows from $W=Fs\cos\theta$. Since $v=\frac{s}{\Delta t}$, dividing work by time gives $P=Fv\cos\theta$. This is instantaneous power when $F$, $v$, and $\theta$ refer to one moment; if they vary, average power must come from total work divided by total time.

Worked Example

A motor does $1.8\times10^4\text{ J}$ of work in $30\text{ s}$:

If a car experiences a forward driving force of $1200\text{ N}$ while travelling at $15\text{ m s}^{-1}$, then:

For example, if a $50\text{ N}$ force acts at $60^\circ$ to a velocity of $4.0\text{ m s}^{-1}$, then $P=(50)(4.0)\cos60^\circ=100\text{ W}$. The perpendicular force component contributes no power because it does no work.

A common misconception is that power is the same as energy. Energy is the amount transferred; power is the rate at which it is transferred. Two machines may do equal work, but the machine completing it faster has greater power.

Exam Technique

For a Calculate question, show the equation, substitution, and final value. Convert time to seconds and energy to joules before calculating, and distinguish watts from joules.