Power

🧭 Plot Summary

Power is a rate, not an amount — it's how quickly energy changes, whether that energy is being transferred into or out of a system or simply converted from one form to another inside it. Two scenarios can transfer the exact same amount of energy and still have wildly different power, just by taking a different amount of time to do it. Average power captures this most directly: P_avg = ΔE/Δt, the energy transferred or converted divided by the time it took. Because work is itself the change in energy of an object or system due to a force, that same idea can be written in terms of work instead: P_avg = ΔW/Δt. But power often isn't constant — a car's engine delivers more power accelerating onto a highway than cruising at a steady speed — so physics also needs an instantaneous version, found by shrinking that time interval down to an instant: P_inst = dW/dt. When the force doing the work is constant and the object's velocity is known, that definition simplifies into a derived shortcut you'll use constantly: P_inst= Fv cosθ, where θ is the angle between the force and the velocity. Average power only equals instantaneous power when the power itself doesn't change over the interval — otherwise they can be very different numbers describing the very same process.

What you'll do in this lesson

• Define power as the rate of energy change — by transfer or by conversion — and distinguish it clearly from energy itself.
• Apply average power from energy transferred, P_avg = ΔE/Δt, and from work done, P_avg = ΔW/Δt.
• Apply the definition of instantaneous power, P_inst = dW/dt, and connect it to slopes and areas on W-t and P-t graphs.
• Derive and apply P_inst = Fv cosθ for the power delivered by a constant force's component parallel to an object's velocity.
• Distinguish average power from instantaneous power, and recognize the one case where they coincide — when power is constant.
• Use a P(t) graph, such as one describing a car accelerating from rest, to reason about work done or velocity over time.

Why it matters

Power closes out Unit 3 by putting a clock on everything you've learned about work and energy — and the AP exam loves to hand you a P(t) or F(t) graph and ask you to reason your way back to work done or velocity, exactly the kind of translation between representations that Mathematical Routines and Translation Between Representations questions are built around.

✅ Self-Check Before You Roll On

Check off each item as you get there. These aren't grades — they're your own signal.