Physics: motion, energy, and waves
Start with measurements, models, and movement before working with forces and energy.
GUIDE8 published lessons · Updated 2026-09-27
Before you begin
Start at lesson 1. No previous physics study is assumed. Read one idea at a time, work through the example on paper, then try the short exercise. Use a calculator when useful. Move on when you can explain the answer, not just repeat it. The opening lessons use everyday descriptions before formulas. Later calculations draw on the linked Mathematics foundations; pause for those prerequisites as needed.
See the pathway from novice to doctoral study · Review the mathematics foundations
Working toward: Choose a relationship, keep units consistent, calculate a prediction, and identify where the model stops applying.
Read each explanation, work through the example, and attempt the exercise before opening its answer. Published lessons are ready to study; unfinished roadmap topics remain planned.
Validation: Original calculation-based examples with explicit assumptions. These lessons do not report physical experiments.
1. Describe a measurement
Before this lesson: No prior subject knowledge. Start here.
Physics starts with questions about things we can observe and measure. A measurement needs both a number and a unit. Length, elapsed time, and mass are different quantities: metres, seconds, and kilograms are common units for them. Record what was measured before choosing a formula. A number on its own is often incomplete.
Worked example
“The book is 24 cm long” identifies the object, the property, the number, and the unit. “It took 6 s” describes elapsed time, not length. These statements can be understood before introducing algebra.
Your turn
A toy car travels along a 2 metre track in 4 seconds. Which number measures length and which measures elapsed time?
Show answer and reasoning
2 metres measures track length. 4 seconds measures elapsed time. Metres and seconds cannot be added to get one total measurement.
Watch for: Measuring tools have limited resolution. Extra digits in a calculator result do not automatically make a measurement more precise.
Link to this lesson2. Choose what the model leaves out
Before this lesson: Read 1. Describe a measurement first; return to its example if the new terms are unfamiliar.
A physical model is a simplified account used to describe or predict something. Simplification can help answer one question while making a model unsuitable for another. State what is being studied, which effects are included, and which are ignored. Compare predictions with evidence; disagreement can point to poor measurements, a calculation error, or a model that does not fit the situation.
Worked example
To estimate a short walk’s duration, a model may assume constant speed. Real walking includes starting, stopping, and turning. The constant-speed assumption is useful for an estimate but cannot describe each step.
Your turn
A model assumes a car moves the same distance every second. Would it describe the car’s motion accurately while the car is stopping at a light? Why?
Show answer and reasoning
No. While stopping, the distance travelled each second decreases. The constant-speed assumption no longer matches that part of the motion.
Watch for: A useful model is not a claim that its simplifying assumptions are exactly true in the world.
Link to this lesson3. Position and elapsed time
Before this lesson: Read 2. Choose what the model leaves out first; return to its example if the new terms are unfamiliar.
Position describes where something is relative to a chosen origin, or zero point. For motion along a straight line, choose a positive direction too. Elapsed time is the time between two readings: subtract the start reading from the end reading. A position reading is different from the distance travelled to reach it.
Worked example
On a straight track, choose the left end as 0 m and rightward as positive. A marker at 3 m is three metres right of the origin. A timer changes from 2 s to 7 s during a movement, so elapsed time is 7 − 2 = 5 s.
Your turn
A timer reads 4 s when motion starts and 10 s when it ends. What is the elapsed time?
Show answer and reasoning
10 − 4 = 6 seconds. The final timer reading is 10 seconds, but this movement lasted 6 seconds.
Watch for: Changing the coordinate origin changes position numbers; it does not move the object.
Link to this lesson4. Speed as distance per second
Before this lesson: Read 3. Position and elapsed time first; return to its example if the new terms are unfamiliar.
For a whole journey, average speed tells you the distance travelled per unit of elapsed time. Divide total distance by total time. The notation m/s means metres per second. First interpret the division in words, then use symbols: average speed = distance ÷ time. This average does not require motion to have been steady at every instant.
Worked example
A toy travels 6 m in 3 s. Sharing the 6 metres across 3 seconds gives 2 metres per second on average: 6 ÷ 3 = 2 m/s. If it travelled steadily, it would cover 2 m in each second.
Your turn
A toy travels 8 m in 4 s. Find its average speed and say what it means.
Show answer and reasoning
8 ÷ 4 = 2 m/s. It covers an average of 2 metres for each second of elapsed time; the actual distance in individual seconds may vary.
Watch for: Use total elapsed time, including stops, when calculating average speed over the entire journey.
Link to this lesson5. Distance, displacement, and velocity
Before this lesson: Read 4. Speed as distance per second first; return to its example if the new terms are unfamiliar.
Distance measures the length of a path; displacement measures the change from starting position to ending position, including direction. Average speed is total distance divided by elapsed time. Average velocity is displacement divided by elapsed time. These averages do not describe every moment of a journey.
Worked example
Walking 30 m east and then 10 m west in 20 s covers 40 m but produces a displacement of 20 m east. Average speed is 2 m/s; average velocity is 1 m/s east.
Your turn
A person walks 12 m north and 12 m south in 16 s. What are the average speed and average velocity?
Show answer and reasoning
Distance is 24 m, so average speed is 24/16 = 1.5 m/s. Displacement is zero, so average velocity is zero. The person was moving despite the zero average velocity.
Watch for: Do not replace total distance with displacement when calculating average speed.
Link to this lesson6. Net force changes velocity
Before this lesson: Read 5. Distance, displacement, and velocity first; return to its example if the new terms are unfamiliar. Mathematics: units, letters, powers, and rearranging equations. Review those linked foundations before calculating.
In a classical constant-mass model, net force equals mass times acceleration: F = ma. Forces add as vectors. Zero net force means zero acceleration, which permits motion at constant velocity. A force does not need to keep acting to maintain constant velocity in this model; friction often masks this in everyday observations.
Worked example
A 2 kg cart experiences 10 N rightward and 4 N leftward. Net force is 6 N rightward; acceleration is 6/2 = 3 m/s² rightward.
Your turn
A 5 kg cart experiences 18 N forward and 8 N backward. Find its acceleration.
Show answer and reasoning
Taking forward as positive, Fnet = 18 − 8 = 10 N. a = Fnet/m = 10/5 = 2 m/s² forward. Other forces are assumed to balance in perpendicular directions.
Watch for: Use net force, not just one applied force. Mass in kilograms and weight in newtons are different quantities.
Link to this lesson7. Kinetic energy and work
Before this lesson: Read 6. Net force changes velocity first; return to its example if the new terms are unfamiliar. Mathematics: units, letters, powers, and rearranging equations. Review those linked foundations before calculating.
For a nonrelativistic object, translational kinetic energy is K = ½mv². Net work changes kinetic energy. A constant force parallel to displacement does work W = Fd; perpendicular force contributes no work along that displacement. Energy bookkeeping depends on the chosen system and on transfers such as heating.
Worked example
A 2 kg cart moving at 3 m/s has K = ½ × 2 × 9 = 9 J. At 6 m/s it has 36 J: doubling speed quadruples kinetic energy.
Your turn
How much net work raises a 4 kg cart’s speed from 2 m/s to 5 m/s?
Show answer and reasoning
ΔK = ½ × 4 × (5² − 2²) = 2 × 21 = 42 J. The required net work is +42 J. This concerns net work, after opposing contributions are included.
Watch for: Do not square the change in speed. The formula uses the difference of squared speeds.
Link to this lesson8. Frequency, wavelength, and wave speed
Before this lesson: Read 7. Kinetic energy and work first; return to its example if the new terms are unfamiliar. Mathematics: units, letters, powers, and rearranging equations. Review those linked foundations before calculating.
For a periodic wave, wave speed equals frequency times wavelength: v = fλ. Frequency counts cycles per second in hertz; wavelength is the distance between corresponding points in successive cycles. A wave can carry energy without transporting the medium bodily along its entire path. Wave speed depends on the medium and conditions.
Worked example
For a sound wave travelling at an assumed 340 m/s with frequency 500 Hz, λ = 340/500 = 0.68 m. At the same wave speed, doubling frequency halves wavelength.
Your turn
A periodic wave travels at 12 m/s with frequency 3 Hz. Find its wavelength and period.
Show answer and reasoning
λ = v/f = 12/3 = 4 m. Period T = 1/f = 1/3 s, approximately 0.333 s. Frequency and period are reciprocals.
Watch for: Sound speed is not universally 340 m/s. Light in vacuum and sound in air have different physical mechanisms and speeds.
Link to this lessonFrom first steps to doctoral study
Start slowly. Each stage builds on the previous one; later branches have their own prerequisites. The foundation lessons are available now. The remaining curriculum is a plan for future lessons, not a complete course.
1. First steps · FOUNDATION LESSONS AVAILABLE
Before you start: No prior physics; everyday counting and reading.
Measurements, models, position, elapsed time, speed, and a first encounter with forces, energy, and waves.
Ready to continue when you can: Explain what is measured, choose units, and state a model’s assumptions.
Start the foundation lessons →2. School foundations · PLANNED
Before you start: First-step physics; algebra and introductory graphs.
Vectors, motion, forces, momentum, energy, thermal phenomena, waves, electricity, circuits, and geometric optics.
Ready to continue when you can: Draw a physical model, choose a relationship, and check units and limiting cases.
3. Undergraduate core · PLANNED
Before you start: Algebra, trigonometry, calculus, and vectors.
Calculus-based mechanics, electromagnetism, oscillations and waves, thermodynamics, modern physics, and experimental methods.
Ready to continue when you can: Derive a prediction, compare it with data, and propagate measurement uncertainty.
4. Advanced undergraduate study · PLANNED
Before you start: Calculus-based core; linear algebra and differential equations.
Analytical mechanics, quantum mechanics, statistical mechanics, advanced electromagnetism, relativity, and computational physics.
Ready to continue when you can: Solve problems through more than one representation and explain approximations and boundary conditions.
5. Graduate foundations · PLANNED
Before you start: Advanced undergraduate theory and mathematical methods.
Graduate classical mechanics, electrodynamics, quantum theory, statistical physics, and specialist mathematical or experimental methods.
Ready to continue when you can: Build sustained derivations and evaluate where a theory or approximation applies.
6. Research specialization · PLANNED
Before you start: Relevant graduate theory and methods.
Choose a branch such as condensed matter, particle physics, astrophysics, optics, plasma physics, or quantum information; develop its experimental or computational skills.
Ready to continue when you can: Reproduce a published result, audit uncertainty, and formulate a testable extension.
7. Doctoral research practice · PLANNED
Before you start: Specialist expertise and suitable research supervision or collaboration.
Original questions, experimental or theoretical design, inference, reproducibility, research communication, and thesis defence.
Ready to continue when you can: Produce and defend an original contribution, comparing it with existing evidence and competing explanations.
Doctoral-level work involves specialization, original research, and expert critique. This pathway supports that preparation; completing site lessons does not confer a degree or establish research competence.
References
Original AUWEN lessons, with upstream documentation for further study and version checks.
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