Nano PHYSICS . MECHANICS . WORK AND ENERGY . POWER

Power as F · v

For a force doing work on an object, instantaneous power is the dot product of force and velocity. Only the component of force along velocity contributes.

Physics · Mechanics · Work and Energy · Power · Power as F · v
Access for this nano-lesson
Unsigned visitors can show & copy prompts for Steps 1-3. Signed-in free accounts can also Run with AI for Steps 1-2. Paid accounts unlock everything (Steps 1-6 + Help prompts + AI).
Steps 1-3 Free Steps 4-6 Paid
STEP 1
Orient: power as f · v
Free
Establish power as the rate of work or energy transfer.
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Goal: define power using work, energy transfer, time, units, and physical meaning.
STEP 2
Conceptual grounding: build the power model
Free
Build a workflow for average power, instantaneous power, force-velocity power, signs, and efficiency.
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Goal: distinguish average power, instantaneous power, force-velocity power, and efficiency.
STEP 3
Real-world connection: interpret energy-transfer rates
Free
Apply power reasoning to elevators, engines, cycling, braking, machines, and losses.
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Goal: explain real mechanical systems using energy-transfer-rate reasoning.
STEP 4
Check your understanding: diagnostic mini-quiz
Paid
Attempt each question before revealing the power reasoning.
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Goal: identify and correct unit, time, force-component, sign, and efficiency errors before they become calculation errors.
STEP 5
Practice: solve increasingly rich power situations
Paid
Apply the model to situations that grow in complexity.
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Goal: write concise, physically justified power calculations and explanations.