How to Use This Guide
- Read the short concept explanation first.
- Study the equation table to learn when each formula should be used.
- Run the activity and then attempt mastery questions without notes.
Integrated Physics
Curriculum Guide
Curriculum Guide
Clear formulas, beginner-friendly explanations, and interactive practice
Curriculum Intent
This guide is built for first-time learners. Every unit starts with plain-language ideas, then moves to equations, then practice. You are expected to show how you think, not only the final answer.
How You Will Be Evaluated
- Good setup and reasoning are prioritized.
- Sketches/graphs/FBDs matter in grading.
- A small arithmetic mistake is less important than a wrong model choice.
Study System
Use this sequence each day: Learn -> Visualize -> Solve -> Check -> Reflect. This keeps the course active and helps you remember concepts for tests and projects.
Progress Tracker
Mark completed checkpoints. Progress is saved on this device.
Core Graphs You Must Read Fluently
Displacement-Time (d-t)
Slope tells you velocity. Steeper line means faster change in position.
Velocity-Time (v-t)
Slope tells you acceleration. Area under the line tells displacement.
Acceleration-Time (a-t)
Flat line above zero means constant positive acceleration.
Free Body Diagrams (FBD) Basics
How to read this: one box is your system. Every arrow is one external force on that system. Then apply \(\Sigma F = ma\) by axis.
Course Map
| Unit | Main Idea | Core Skill | PDF Link |
|---|---|---|---|
| 1. Position and Velocity | Where objects are and how they move | Graph reading and motion language | Pages 1-12 |
| 2. Acceleration | How velocity changes | Kinematics setup and equation choice | Pages 13-15 |
| 3. Projectile Motion | 2D motion with gravity | Separate x and y reasoning | Pages 16-24 |
| 4. Forces | Why motion changes | Free body diagrams and net force | Pages 25-38 |
| 5. Momentum | Collisions and impulse | Conservation modeling | Pages 39-44 |
| 6. Energy | Tracking kinetic and potential energy | Energy bookkeeping | Expanded continuity |
Lab Quizzes
Before Lab
Short check on units, symbols, and setup choices.
During Lab
One graph plus one explanation question while data is collected.
After Lab
Reflection: what assumption was strongest and what limitation mattered most?
Exam Blueprint
Weighting
- Lab quizzes: 10%
- Tests and projects: 90%
How Tests Are Graded
- Understanding of concept over final numeric answer.
- Correct model choice and method steps are critical.
- Clear reasoning and diagrams can earn strong credit.
Unit 1: Position and Velocity
This is your foundation unit. If you understand this unit deeply, every other unit gets easier.
1.1 Position and Displacement
Position tells where something is. Displacement tells how far and in what direction position changed.
Think of it like this: distance is "how much path you walked," displacement is "where you ended compared to where you started."
1.2 Distance, Speed, and Velocity
Speed is how fast (no direction). Velocity is how fast with direction. A trip out and back can have high speed but zero displacement, so average velocity can be zero.
1.3 d-t and v-t Graph Basics
On a displacement-time graph, slope gives velocity. On velocity-time graph, area gives displacement.
Beginner tip: ask "What are the axes?" before reading any graph. Most mistakes start by reading the wrong axis meaning.
1.E Equation Sheet
| Equation | What It Means | When to Use | Common Mistake |
|---|---|---|---|
| \(\Delta d = d_f - d_i\) | Displacement from start and end positions | You know starting and ending position | Using total path distance in place of displacement |
| \(v_{avg} = \dfrac{\Delta d}{\Delta t}\) | Average velocity over a time interval | You know displacement and time change | Using distance instead of displacement |
| \(d_f = d_i + vt\) | Uniform motion model (constant velocity) | No acceleration in interval | Using when velocity is changing |
| \(\Delta d = \text{area under }v\text{-}t\) | Displacement from velocity graph | Graph-based motion problems | Treating area as final position instead of change |
1.A Activity: Motion Change Calculator
Use this to practice the meaning of displacement and average velocity.
Result will appear here.
1.M Mastery Check
Q1. You walk 8 m east then 3 m west. Distance and displacement?
Distance = 11 m. Displacement = +5 m east.
Q2. Why can average velocity be zero while speed is not zero?
Because velocity depends on displacement, which can cancel out on a round trip.
Unit 2: Acceleration
Acceleration tells how quickly velocity changes. This includes speeding up, slowing down, and changing direction.
2.1 What Acceleration Means
If velocity changes with time, acceleration exists. Positive/negative signs depend on your chosen axis direction.
2.2 v-t and a-t Graph Basics
Velocity-time slope gives acceleration. Area under velocity-time gives displacement. Acceleration-time area gives change in velocity.
2.3 Constant vs Changing Acceleration
When acceleration is constant, use constant-acceleration equations. If acceleration changes a lot, use graph methods or shorter intervals.
2.E Equation Sheet
| Equation | What It Means | When to Use | Common Mistake |
|---|---|---|---|
| \(a = \dfrac{\Delta v}{\Delta t}\) | Average acceleration | Known velocity change and time | Losing sign (+/-) |
| \(v_f = v_i + at\) | Final velocity for constant acceleration | Known \(v_i\), \(a\), \(t\) | Using when acceleration is not constant |
| \(\Delta d = v_i t + \dfrac{1}{2}at^2\) | Displacement with constant acceleration | Known \(v_i\), \(a\), \(t\) | Forgetting the \(\frac{1}{2}\) |
| \(\Delta d = \text{area under }v\text{-}t\) | Graph displacement method | Graph questions and nonuniform segments | Ignoring negative area regions |
2.A Activity: Constant Acceleration Solver
Enter values for \(v_i\), \(a\), and \(t\). The tool computes \(v_f\) and \(\Delta d\).
Solution output will appear here.
2.M Mastery Check
Q1. A car slows from 22 m/s to 10 m/s in 4 s. Find acceleration.
\(a = (10-22)/4 = -3\,\text{m/s}^2\).
Q2. Why can acceleration be negative?
Negative means direction on your chosen axis, not "bad" or "small" acceleration.
Unit 3: Projectile Motion
Projectile motion is easier when you split it into two simpler motions: horizontal and vertical.
3.1 Horizontal and Vertical Motion
Uniform horizontal movement means horizontal velocity stays constant, so horizontal position changes at a steady rate.
Why? In ideal projectile motion, gravity acts downward, not sideways, so it does not change horizontal velocity.
3.2 Trajectory and Time
Trajectory is the path in space (x-y). It looks like a curve. Do not confuse it with a graph against time.
3.3 Circular Motion Connection
Circular motion helps you see that velocity can change direction even when speed is steady.
3.E Equation Sheet
| Equation | What It Means | When to Use | Common Mistake |
|---|---|---|---|
| \(\Delta x = v_x t\) | Horizontal displacement | Projectile horizontal axis | Adding gravity term to x-motion |
| \(v_y = v_{iy} + gt\) | Vertical velocity update | Vertical projectile motion | Wrong sign for \(g\) |
| \(\Delta y = v_{iy}t + \dfrac{1}{2}gt^2\) | Vertical displacement | Vertical position change | Using \(v_x\) instead of \(v_{iy}\) |
| \(a_c = \dfrac{v^2}{R}\) | Centripetal acceleration magnitude | Uniform circular motion | Thinking acceleration points tangent |
3.A Activity: Projectile Sandbox
Assumes same launch and landing height. Enter launch speed and angle.
Range/time/height output will appear here.
3.M Mastery Check
Q1. Why is projectile horizontal motion uniform in the ideal model?
Because no horizontal force is included; gravity acts only vertically.
Q2. If two objects start at same height, one dropped and one thrown horizontally, which lands first (ideal case)?
They land at the same time because vertical motion is independent of horizontal motion.
Unit 4: Forces
Forces explain why motion changes. This unit focuses on clear diagrams and direction-based thinking.
4.1 Newton's Laws in Simple Words
- 1st law: no net force -> keep doing what you are already doing.
- 2nd law: more net force means more acceleration for same mass.
- 3rd law: forces come in pairs on different objects.
4.2 Free Body Diagrams (FBD)
An FBD is a picture of one object and all forces acting on it. It helps avoid equation mistakes.
Start with this question: "Which way is acceleration?" Then your net force must point that way.
4.3 Net Force and Motion Direction
If rightward forces are larger than leftward forces, acceleration is rightward. If balanced, acceleration is zero.
4.E Equation Sheet
| Equation | What It Means | When to Use | Common Mistake |
|---|---|---|---|
| \(\Sigma F = ma\) | Net force causes acceleration | Any force-motion setup | Using one force instead of net force |
| \(W = mg\) | Weight force near Earth | Vertical force analysis | Mixing up mass and weight |
4.A Activity: Net Force Direction Tool
Enter rightward and leftward total forces. Tool returns net force and acceleration direction.
Net force output will appear here.
4.M Mastery Check
Q1. If net force is zero, can the object still move?
Yes, it can move at constant velocity with zero acceleration.
Q2. Why is FBD usually the first step before equations?
Because it clarifies which forces exist and their directions, preventing wrong equation setup.
Unit 5: Momentum
Momentum explains collisions very effectively. This unit connects directly to safety examples like airbags and landing surfaces.
5.1 Momentum and Impulse
Momentum depends on mass and velocity. Impulse is force applied over time and equals change in momentum.
5.2 Collision Types
Elastic and inelastic collisions both conserve momentum in closed systems. The big difference is whether kinetic energy stays the same.
5.3 Conservation in Real Cases
Always set a direction sign first. Many collision mistakes come from inconsistent signs.
5.E Equation Sheet
| Equation | What It Means | When to Use | Common Mistake |
|---|---|---|---|
| \(p = mv\) | Linear momentum | Any momentum setup | Ignoring direction sign in velocity |
| \(J = F\Delta t\) | Impulse from average force | Known force duration | Mixing up units |
| \(J = \Delta p\) | Impulse-momentum link | Velocity change problems | Dropping initial velocity sign |
| \(\Sigma p_i = \Sigma p_f\) | Momentum conservation | Closed-system collisions | Applying when strong external force acts |
| \(v_f = \dfrac{m_1v_1 + m_2v_2}{m_1+m_2}\) | Perfectly inelastic final speed | Objects stick together | Using for non-sticking collisions |
5.A Activity: Collision Calculator
Choose collision type and compare outcomes.
Collision output will appear here.
5.M Mastery Check
Q1. Why do airbags reduce force on passengers?
They increase collision time, so average force is smaller for the same momentum change.
Q2. Is momentum conserved in inelastic collisions?
Yes, in a closed system, momentum is conserved even if kinetic energy changes.
Unit 6: Energy
This unit helps you track energy states simply: motion energy and height energy. It connects strongly to earlier kinematics and forces units.
6.1 Kinetic and Gravitational Energy
Kinetic energy depends on speed. Gravitational potential energy depends on height in a chosen reference system.
6.2 Conservation Idea
If losses are small, total mechanical energy stays about constant while energy shifts between forms.
6.3 Power as Energy Rate
Power tells how quickly energy changes over time.
6.E Equation Sheet
| Equation | What It Means | When to Use | Common Mistake |
|---|---|---|---|
| \(K = \dfrac{1}{2}mv^2\) | Kinetic energy | Moving objects | Forgetting to square \(v\) |
| \(U_g = mgh\) | Gravitational potential energy | Near-Earth height change | Not stating height reference level |
| \(E_{mech} = K + U_g\) | Mechanical energy total | Track two energy stores | Mixing signs and reference levels |
| \(P = \dfrac{\Delta E}{\Delta t}\) | Power as energy-rate | Rate/effort comparisons | Using wrong energy interval |
6.A Activity: Energy Budget Tool
Compute \(K\), \(U_g\), and total mechanical energy for a chosen state.
Energy output will appear here.
6.M Mastery Check
Q1. If speed doubles, what happens to kinetic energy?
It becomes 4 times larger because \(K\propto v^2\).
Q2. Why do we choose a reference level for \(U_g\)?
Because potential energy is relative; only changes in \(U_g\) are physically meaningful.
Physics Quickfire Studio
Fast question game for concept recall. Designed for beginners to check understanding in short bursts.
Press Start to begin quickfire.
Score: 0 / 0