Read the force graph
Connect force values with positions rather than elapsed times.
AP Physics 1 · Unit 3 · Work, Energy, and Power
Work Done by Varying Forces
Read force–position graphs and use their signed areas to calculate work when the force changes during a motion.
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Learn by doing
Three ideas you’ll put into motion
Add signed areas
Use simple geometric regions to find positive, negative, and net work.
Predict the energy change
Connect the total work from a changing force with the object’s kinetic energy.
The big idea
The key ideas, at a glance.
Area represents work
The signed area under a force-component-versus-position graph gives work along that coordinate. A force–time graph instead gives impulse.
Opposing regions can cancel
Areas below the position axis contribute negative work. Add all signed regions to find the net work and corresponding ΔK.
A quick comparison
A constant +3 N force acts through a +2 m displacement.
Rectangular area → +6 J of work.
Teaching this topic?Classroom fit, AP connections, and support
- Classroom fit
- Use for a concept introduction, guided independent practice, or a projected class discussion.
- Before students begin
- Work, kinetic energy, and the areas of rectangles and triangles. Calculus is not needed.
- Built-in support
- Prepared scenes, guided prompts, and feedback on lesson questions.
- AP Physics 1 connections
- Unit 3: graphical work calculations and the work–kinetic energy theorem.
- Check for understanding
- Ask how the area interpretation differs between a force–position graph and a force–time graph.
Ready to test your thinking?
The first scene is set up. Start the lesson and explore.