Why code makes physics easier

You can read a formula for falling, but it is harder to spot its behaviour until you run it repeatedly. Code turns one relationship into a table, a picture, and a set of tests without changing the underlying physics.

Think like a programmer

A physics model is like a pure function. Give it a starting condition and a time; it returns a prediction. A simulation is the loop that calls that function for many times.

Model checklist

Inputs: Starting height in metres and time in seconds.
State: The current time; position can be calculated from it.
Rule: Gravity increases downward speed at 9.81 m/s².
Output: Distance fallen and landing time.
Check: At time zero, the distance must be zero.

For an object released from rest near Earth, the distance it has fallen is:

\[d=\\frac{1}{2}gt^2\]

Here d is distance in metres, g is gravity in metres per second squared, and t is time in seconds. Notice the square: doubling time makes the distance four times as large.

Formula, data, and motion

This is one model shown three ways. The object starts at rest; air resistance is not included.

Starting height: 20 m

distance = ½ × 9.81 × time²

Time (s)	Fallen (m)
0.00	0.00
0.50	1.25
1.01	5.00
1.51	11.25
2.02	20.00

Landing time: 2.02 s

function distanceFallen(timeSeconds: number) {
  return 0.5 * 9.81 * timeSeconds ** 2;
}

Try this experiment

Prediction: If you double the height, the landing time will not double.

Set the height to 10 m and record the time. Then set it to 40 m. Compare the two times and explain the square-root relationship.

Where this model breaks

This model assumes constant gravity, no air resistance, and a release from rest. A parachute, a thrown ball, or a long fall needs a different model.

Summary

Code does not make a formula more true. It makes repeated calculations, checks, and visual comparisons cheap enough to inspect. The formula is still the model; the diagram is only its output.

Glossary

Model: a limited rule used to make a prediction.
Simulation: code that evaluates a model across time or many cases.
Initial condition: the state supplied at the beginning.

Self-check

What input does distanceFallen need?
What result must it return at time zero?
Which omitted force matters for a feather?

Sources

NIST, The International System of Units (SI).

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 Why Code Makes Physics Easier, write down the quantities you can control, the values your program must retain, and the result a reader could inspect. In Physics as Computation, 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 Why Code Makes Physics Easier 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 Why Code Makes Physics Easier into a test

See one falling-object model as an equation, computed data, and a motion diagram, then learn what code adds.

Name the inputs and units that the physics as computation 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.

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