Relative motion
Motion is always measured relative to a reference frame. A passenger walking forward on a train has one velocity relative to the train and another relative to the ground.
Think like a programmer
Model checklist
- Inputs
- Observed body state, observer state, and time.
- State
- Initial positions and velocities for both bodies.
- Rule
- Subtract observer position and velocity from observed values.
- Output
- Relative position and velocity.
- Check
- A body is stationary relative to itself.
One event, two frames
Switch the observer frame. The walker is the same object, but relative position and velocity depend on which state you subtract.
In the ground frame at 0.0 s: walker position [2.0, 0.0] m; velocity [1.0, 0.0] m/s.
const relativeVelocity = addVectors(walker.velocity, scaleVector(train.velocity, -1));
Try this experiment
Prediction: The walker moves backward in the train frame because the train is faster relative to the ground.
Switch frames at the same time. Compare both status values and identify exactly which observer velocity the program subtracts.Where this model breaks
Summary
Keep each observer's state explicit. Relative motion is a subtraction operation with a declared frame, not a disagreement about the event.
Glossary
- Reference frame: an observer's coordinate system and clock.
- Relative velocity: velocity measured by one observer for another body.
- Galilean transformation: the ordinary low-speed change between constant-velocity frames.
Self-check
- Which state is subtracted to change frames?
- What is a body's velocity relative to itself?
- When does this simple transformation stop applying?
Sources
- OpenStax, University Physics Volume 1, relative motion chapter.
Model contract
Treat the lesson as a small function before treating it as a fact to memorize. Give every value a unit, keep only the state needed for the next step, and make the output easy to inspect.
\[\text{observable output} = f(\text{inputs},\,\text{state})\]- Inputs
- Quantities you set or measure, with units and useful bounds.
- State
- Values the program must retain to reproduce the next result.
- Rule
- The relationship or update that turns inputs and state into a result.
- Check
- A known limit, unit check, invariant, or measured result that can expose a bad model.
Implement the idea as a model
For Relative Motion, write down the quantities you can control, the values your program must retain, and the result a reader could inspect. In Motion in 2D and 3D, the useful program is not the drawing: it is the smallest explicit model that makes a prediction you can test.
Guided experiment
Prediction: changing one declared input while holding the others fixed should change only the outputs that the model connects to that input. Choose one input, predict the direction of change, then check a limiting case such as zero, a symmetric arrangement, or a familiar low-speed or small-change approximation.
Where this model breaks
This lesson is a teaching model, not a complete simulator. Before using it outside the stated question, check which interactions, scales, uncertainties, boundary conditions, and measurement limits it leaves out.
Summary
Treat Relative Motion as a contract: named inputs and units enter a rule, the rule produces an observable result, and a known limit or invariant checks whether the implementation deserves trust.
Glossary
- Input: a measured value or chosen parameter supplied to a model.
- State: the smallest set of values needed to continue or reproduce a model.
- Validation: comparing an output with a known result, limit, invariant, or measurement.
Self-check
- Which values are inputs, and which values must remain state?
- What observable result would tell you the model is behaving as expected?
- Which assumption would you test first before applying the model to a real system?
Model review: turn Relative Motion into a test
Switch between ground and train frames to compute relative position and velocity by subtracting observer state.
- Name the inputs and units that the motion in 2d and 3d model needs.
- Separate the state you must keep from values you can calculate when needed.
- Write one rule that maps the current state and inputs to an observable result.
- Choose a limiting case, unit check, invariant, or known result before trusting an output.
- State one assumption you would change before using this simplified model for a real decision.