How fast is energy transferred or work done, and how is that rate calculated?
Topic 3.5 Power: define power as the rate of energy transfer through P = W/t = Delta E/Delta t, and use P = Fv to relate power to force and speed.
A focused answer to AP Physics 1 Topic 3.5, covering power as the rate of doing work or transferring energy, the formulas P = W/t and P = Fv, average versus instantaneous power, and the watt as a unit, with full worked examples.
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What this topic is asking
The College Board (Topic 3.5) wants you to define power as the rate at which work is done or energy is transferred, , to use the relationship for a force acting on a moving object, and to distinguish average power (over an interval) from instantaneous power (at an instant). Power is measured in watts.
The definition of power
Power answers a different question from work. Work (or energy transferred) is how much; power is how fast. Two cranes that each lift a load to the same height do the same work, but the faster one is more powerful. A W light bulb converts J of electrical energy to light and heat every second.
Average and instantaneous power
For a car accelerating from rest, the instantaneous power grows as the car speeds up (more energy delivered per second at higher speed), even if the driving force is roughly constant. The average power over the whole acceleration is the total kinetic energy gained divided by the time taken.
Power as force times speed
A particularly useful form comes from combining with :
since is the speed . When the force is along the motion, this simplifies to . This form is the key to many exam questions: a vehicle moving at constant speed against a resistive force, a motor winding in a cable, a person climbing stairs. It also explains an everyday fact: to move faster against the same resistance, an engine must deliver more power, because rises with speed. The deeper connection is that power unifies the whole unit. Work, kinetic energy, and potential energy all measure quantities of energy; power measures the rate at which those quantities change. Whenever a problem mentions "how long", "per second", or "at what rate", power is the tool, and you can reach for either (when you know the energy and time) or (when you know the force and speed). Recognizing which form a question hands you the data for is the main skill, and the two forms are always consistent because both come from the definition of power as energy per unit time.
Try this
Q1. A pump does J of work in s. Calculate its power output. [2 points]
- Cue. W.
Q2. A N force pushes an object at a constant m/s in the direction of the force. Calculate the power delivered. [2 points]
- Cue. W.
Exam-style practice questions
Practice questions written in the style of College Board exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
AP 2024 (style)4 marksSection II (short FRQ, quantitative). A motor lifts a kg load vertically at a constant speed of m/s. Take m/s squared. (a) Calculate the force the motor must exert. (b) Calculate the power output of the motor. (c) Explain why the power would be greater if the load were lifted at a higher constant speed.Show worked answer →
A 4-point FRQ on power as force times speed.
(a) Force (1 point): at constant speed the motor's force balances the weight: N.
(b) Power (2 points): the force and velocity are both upward, so W.
(c) Explain (1 point): power is . The lifting force (the weight) is fixed, so a higher speed means the same energy is delivered in less time, increasing the rate of energy transfer and hence the power.
Markers reward for the force, for the power, and a rate-based reason linking higher speed to greater power.
AP 2022 (style)1 marksSection I (multiple choice). Two motors raise identical loads through the same height, but motor X does it in half the time of motor Y. How do their power outputs compare? (A) X has half the power (B) they have equal power (C) X has twice the power (D) X has four times the power. Justify your reasoning.Show worked answer →
A 1-point MCQ on power as a rate. The answer is (C).
Both motors do the same work (same load, same height), but power is work divided by time, . Halving the time for the same work doubles the power, so motor X is twice as powerful. The trap is thinking equal work means equal power; power also depends on how quickly the work is done.
Related dot points
- Topic 3.2 Work: calculate the work done by a force through W = Fd cos(theta), connect net work to the change in kinetic energy, and read work as the area under a force-displacement graph.
A focused answer to AP Physics 1 Topic 3.2, covering work as a force acting through a displacement, the formula W = Fd cos(theta), positive and negative work, the work-energy theorem, and work as the area under a force-displacement graph, with full worked examples.
- Topic 3.1 Translational Kinetic Energy: define the kinetic energy of a moving object through K = 1/2 mv^2, and reason about how it changes with mass and speed.
A focused answer to AP Physics 1 Topic 3.1, covering translational kinetic energy, the formula K = 1/2 mv^2, why kinetic energy is a scalar that depends on the square of the speed, and how it varies with mass and reference frame, with full worked examples.
- Topic 3.3 Potential Energy: define potential energy as stored energy of a system's configuration, and calculate gravitational potential energy (mgh) and elastic potential energy (1/2 kx^2).
A focused answer to AP Physics 1 Topic 3.3, covering potential energy as stored energy of a configuration, gravitational potential energy mgh near Earth, elastic potential energy 1/2 kx^2, the role of conservative forces and reference points, with full worked examples.
- Topic 3.4 Conservation of Energy: apply conservation of mechanical energy to systems with conservative forces, and account for energy dissipated by nonconservative forces such as friction.
A focused answer to AP Physics 1 Topic 3.4, covering conservation of mechanical energy, the interchange of kinetic and potential energy, how friction and other nonconservative forces dissipate energy, and using energy bookkeeping to solve problems, with full worked examples.
- Topic 2.5 Newton's Second Law: relate the net force on an object to its acceleration and mass through Fnet = ma, and use it to solve for forces, masses or accelerations.
A focused answer to AP Physics 1 Topic 2.5, covering Newton's second law, the proportionality of acceleration to net force and inverse proportionality to mass, applying it axis by axis, and solving multi-force problems, with full worked examples.
Sources & how we know this
- AP Physics 1: Algebra-Based Course and Exam Description — College Board (2024)