Calculate power and derive P = Fv
Calculate power as work or energy transferred per unit time and connect it to force and velocity.
Section 5 · Work, energy and power
AS Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 5. These original explanations and calculations support theory study; full timed assessment and human subject-teacher review remain outstanding.
Before you begin
- Use force, displacement, speed, mass and gravitational field strength with consistent SI units.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which unit measures power?
What you will learn
- Define power as work done per unit time
- Use P = W/t
- Derive and apply P = Fv when force and velocity are in the same direction
Power describes the rate of energy transfer
Power is the work done per unit time: P = W/t. Since work is an energy transfer, power is also energy transferred per unit time. Its SI unit is the watt, where 1 W = 1 J s⁻¹.
For the same work, completing it in less time requires greater average power. Use the duration of the transfer, not the total time the system has existed.
Derive the force-speed form
For a constant force acting along the direction of motion, work done W = Fs. Substitute into P = W/t to obtain P = Fs/t. Since speed v = s/t, P = Fv.
The force and velocity must be in the same direction for this simple magnitude form. If a force is not parallel to velocity, only its component along the velocity contributes to the power transferred by that force.
Pause and explain
How does P = Fv follow for a force parallel to motion?
Worked example
A motor does 2400 J of work in 20 s. Find its average power. Then find the power from a 300 N driving force at 4.0 m s⁻¹ in the same direction.
Show the worked solution
- P = W/t = 2400/20 = 120 W.
- For parallel force and velocity, P = Fv.
- P = 300 × 4.0 = 1200 W for the second situation.
Answer Average power in the first situation is 120 W; power in the second is 1.2 kW.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A crane transfers 18 kJ of energy in 30 s. Calculate its average power.
Give me a hint
Convert kilojoules to joules before dividing by time.
Compare my reasoning
- 18 kJ = 18 000 J.
- P = W/t = 18 000/30.
- Give power in watts.
600 W.
Look for these in your work
- Energy converted to joules
- Work divided by time
- W unit stated
A car moves at 12 m s⁻¹ while its engine exerts a forward force of 1500 N. Calculate the power delivered by this force.
Give me a hint
The force is parallel to velocity, so use P = Fv.
Compare my reasoning
- P = Fv.
- P = 1500 × 12.
- Convert to kilowatts if useful.
18 000 W = 18 kW.
Look for these in your work
- Force-speed relation applied
- Product correct
- Power unit included
An object moves upward at constant speed 2.0 m s⁻¹ while a 500 N lifting force acts upward. Find the lifting power and explain the role of gravity if the object has constant speed.
Give me a hint
Use the force component along motion; constant speed means zero resultant force.
Compare my reasoning
- P = Fv = 500 × 2.0 = 1000 W.
- At constant speed, the resultant force is zero.
- For a vertical lift with no other vertical forces, weight balances the lifting force; gravity does negative work on the upward displacement.
The lifting force transfers energy at 1.0 kW. At constant speed the net force is zero; the lifting force balances weight, and gravity transfers energy oppositely to the motion.
Look for these in your work
- Power calculated
- Constant-speed force balance used
- Gravity's opposite energy transfer noted
Common mistakes
- Using P = Fv when force is not along velocity without resolving components
- Confusing work in joules with power in watts
- Multiplying force by time instead of displacement or velocity
What can you explain now?
Which unit measures power?
Compare with the explanation
W
A watt is one joule transferred per second.
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Make it stick
Which motion direction must be used when applying P = Fv to one force?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.