Manual Motion Manual

Becoming the Processor: Iterative Physics Worksheet

Physics Lab 01

v1.0.24

Student Name

Date

Part 1: The Iterative Loop

In physics simulations, we don't solve for \(x\) using a single equation. Instead, we perform a loop where we calculate the next state based on the current one.

// The Physics Loop (dt = time step)

1. Calculate position: x_new = x_old + (v_old * dt)

2. Calculate velocity: v_new = v_old + (a * dt)

3. Update time: t_new = t_old + dt

Scenario A: The Constant Cruiser

Initial: \(x = 0\) m, \(v = 5\) m/s, \(a = 0\) m/s², \(dt = 2.0\) s

Step	Time (s)	Pos (m)	Vel (m/s)
0	0.0	0.0	5.0
1
2
3

Scenario B: The Braking Bus

Initial: \(x = 0\) m, \(v = 20\) m/s, \(a = -4\) m/s², \(dt = 1.0\) s

Step	Time (s)	Pos (m)	Vel (m/s)
0	0.0	0.0	20.0
1
2
3

Part 2: Code Breakdown

1. Why do we use the "old" velocity to find the "new" position in our algorithm?

2. In Scenario B, what is the object's position at \(t = 3.0\)s using the kinematic formula \(x = x_0 + v_0 t + \frac{1}{2}at^2\)? How does this compare to your iterative result?

3. If we wanted to make our "guess" more accurate, should we make \(dt\) larger (e.g., 5.0s) or smaller (e.g., 0.1s)? Explain why.

Reference: The Euler Method

This iterative method is formally known as Euler Integration. It is the simplest numerical method for solving differential equations (physics laws!).

In real game engines (like Unity or Unreal), they often use more complex versions like Runge-Kutta or Verlet Integration because they are more stable for large time steps, but the core "loop" logic remains the same.

Physics is just a
loop of small changes.

Computational Motion Modeling

The Logic of Iteration

Coding Constant Velocity

Modeling Uniform Acceleration

Non Constant Acceleration

Motion Prediction Challenge

Algorithm Anatomy Slides

Manual Motion Worksheet

Iterative Logic Guide

Code Constant Slides

Spreadsheet Speedsters Guide

Acceleration Loop Slides

Parabola Programmer Lab

Air Resistance Slides

Terminal Velocity Tracker

Mission Control Slides

Rocket Landing Log

Model Mastery Rubric

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