--- title: "Power as Force Times Velocity, and Efficiency" description: "Dividing work by time when the force is steady gives P = Fv, which reads power straight off a speed. Efficiency then compares the useful output with the total input for the same machine." canonical: https://lightmysky.com/learn/science/power-as-force-times-velocity-and-efficiency-mt_2FFGLIjgV6 source: https://lightmysky.com/learn/science/power-as-force-times-velocity-and-efficiency-mt_2FFGLIjgV6.md retrieved: 2026-09-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Power as Force Times Velocity, and Efficiency Dividing work by time when the force is steady gives P = Fv, which reads power straight off a speed. Efficiency then compares the useful output with the total input for the same machine. Subject: Science · Area: Energy · Ages 17 to 18 Page: https://lightmysky.com/learn/science/power-as-force-times-velocity-and-efficiency-mt_2FFGLIjgV6 ## Ready when they can - Uses P = Fv for a vehicle held at constant speed against a stated resistive force - Moves between the work-over-time and force-times-velocity forms and says when each is easier - Calculates efficiency as a ratio and names where the rest of the input went ## Lesson: Power now, efficiency after Power tells how fast work gets done, not how much work there is in total. It is work divided by time, and the unit is the watt. One watt is one joule per second. A powerful engine and a weak one can shift the same load, but the powerful one finishes sooner. **Example.** For a push along the motion, instant power is force times speed. A cyclist holds 8 metres per second against 30 newtons of drag. Multiply 30 by 8 to get 240 watts. At steady speed the driving force matches the drag, so drag times speed gives the power. No machine is perfect. Efficiency is useful output over total input, always below one. The rest is wasted, mostly as heat and sound. Muscles run near a quarter, and the rest warms the skin. Name where the waste went to turn a bare ratio into a diagnosis. **Tip.** Work over time suits whole jobs with times and energies. Force times velocity suits a snapshot with known speed and thrust. Both are the same physics, since work is force times distance and distance over time is velocity. **Recap.** Read power off work over time or force times speed, and score machines by useful output over input. ## Practice 8 questions on this page, each with its working shown. ## Needs first - [Work Done by a Force at an Angle](https://lightmysky.com/learn/science/work-done-by-a-force-at-an-angle-mt_OvBtur6dW5) ## Opens up - [Elastic and Inelastic Collisions](https://lightmysky.com/learn/science/elastic-and-inelastic-collisions-mt_JMwUuh1YUq)