# Welcome Back - Let's Catch Up!

If you missed any of the first three lessons in this unit, this remix lesson is your fast track back. We are going to hit the highlights of all three lessons in one session. By the end, you will have the key ideas and vocabulary you need to stay on track with the rest of the unit.

Here is what we are covering: 1. Lesson 1 - Describing Motion: position, reference points, speed, velocity 2. Lesson 2 - Graphing Motion: position-time graphs, slope, reading motion stories 3. Lesson 3 - Forces and Newton's Laws: forces, balanced vs. unbalanced, the three laws

Plus a bonus section on energy and simple machines from the unit's broader themes.

Let's go!

# Part 1: Describing Motion (Lesson 1 Recap)

## Motion and Reference Points

Motion is a change in an object's position relative to a reference point. Without a reference point, you cannot say whether something is moving. A passenger on a bus is not moving relative to the bus seat, but is moving relative to a tree outside the window. Both are true at the same time.

Position describes an object's location using both distance and direction from a reference point. "The gym is 200 meters north of the cafeteria" is a complete position description.

## Speed and the s = d/t Formula

Speed is how far an object travels per unit of time. The formula is:

$$s = \frac{d}{t}$$

- Constant speed: equal distances in equal time intervals - Average speed: total distance ÷ total time (most common in calculations) - Instantaneous speed: the speed at one specific moment (what a speedometer shows)

Example: A cyclist rides 45 km in 3 hours. Average speed = 45 / 3 = 15 km/h.

## Speed vs. Velocity

Speed answers "how fast?", it is a number with units (60 mph, 10 m/s).

Velocity answers "how fast AND which direction?", it is speed plus direction (60 mph north, 10 m/s east).

Two cars traveling at 60 mph have the same speed. If one heads north and the other south, they have opposite velocities. A race car circling an oval track at constant speed still changes velocity constantly because its direction is always changing.

# Part 2: Graphing Motion (Lesson 2 Recap)

## Reading Position-Time Graphs

A position-time graph plots an object's distance from a starting point (y-axis) against time (x-axis). The shape of the line tells the whole story:

| Line Shape | What It Means | |---|---| | Straight line going up (steep) | Moving away fast, high constant speed | | Straight line going up (gentle) | Moving away slowly, low constant speed | | Horizontal (flat) line | At rest, position not changing | | Straight line going down | Moving back toward the starting point | | Curved line getting steeper | Speeding up (accelerating) | | Curved line getting flatter | Slowing down (decelerating) |

## Slope = Speed

The most important rule in graph reading: the slope of the line equals the object's speed.

$$\text{speed} = \text{slope} = \frac{\Delta d}{\Delta t} = \frac{d_2 - d_1}{t_2 - t_1}$$

Example: A line passes through (0 s, 0 m) and (5 s, 30 m). Slope = (30 - 0) / (5 - 0) = 30 / 5 = 6 m/s

## Comparing Objects on the Same Graph

When two objects appear on the same graph: - The steeper line = the faster object - Where the lines cross = the two objects are at the same place at the same time

# Part 3: Forces and Newton's Laws (Lesson 3 Recap)

## What Is a Force?

A force is a push or pull on an object. Forces are measured in newtons (N). Every force has both a size (how strong) and a direction (which way).

## Net Force: Balanced vs. Unbalanced

The net force is the combined result of all forces acting on an object.

- Same direction: add the forces. Two people each pushing a box with 10 N in the same direction = 20 N net force. - Opposite directions: subtract. 20 N right vs. 8 N left = 12 N to the right.

Balanced forces → net force = 0 → no change in motion (the object stays still or keeps moving at the same speed)

Unbalanced forces → net force ≠ 0 → motion changes (the object speeds up, slows down, or changes direction)

## Newton's Three Laws

First Law (Inertia): An object at rest stays at rest; an object in motion stays in motion, unless acted on by an unbalanced force. Objects resist changes in their motion. This resistance is called inertia. More mass = more inertia. Seatbelts exist because of this law.

Second Law (F = ma): The acceleration of an object depends on the net force and the object's mass.

$$F = m \times a$$

More force → more acceleration. More mass → less acceleration (for the same force).

Example: Net force = 24 N, mass = 6 kg → a = 24 / 6 = 4 m/s²

Third Law (Action-Reaction): For every action there is an equal and opposite reaction. Forces always come in pairs, acting on different objects. When you walk, your foot pushes back on the ground; the ground pushes your foot forward. That forward push is what moves you.

# Part 4: Energy and Simple Machines (Unit Theme Recap)

## Kinetic and Potential Energy

Energy is the ability to do work. Mechanical energy comes in two main forms:

Kinetic energy (KE) is the energy of motion. Any object that is moving has kinetic energy. A rolling bowling ball has kinetic energy. A flying soccer ball has kinetic energy. The faster an object moves, or the more mass it has, the more kinetic energy it carries.

Potential energy (PE) is stored energy based on position or condition. An object held above the ground has gravitational potential energy, it has the potential to fall and move. A stretched rubber band has elastic potential energy. The higher an object is lifted, or the more massive it is, the more gravitational potential energy it stores.

## Energy Transfer

Energy is constantly converting between kinetic and potential forms:

- A ball at the top of a ramp: mostly potential energy - The same ball rolling at the bottom of the ramp: mostly kinetic energy - At the halfway point: a mix of both

Total mechanical energy (KE + PE) is conserved throughout the motion (ignoring friction).

## Work

In science, work has a precise meaning. Work is done when a force moves an object in the direction of the force. The formula is:

$$W = F \times d$$

where W = work (in joules, J), F = force (in newtons), and d = distance the object moves (in meters).

If you push a box and it does not move, you have done zero work on the box, no matter how hard you pushed. Displacement must occur for work to be done.

Example: You push a box with 15 N of force and it slides 4 meters. Work = 15 × 4 = 60 joules.

## Simple Machines

A simple machine is a device that changes the direction or size of a force, making it easier to do work. Simple machines do not reduce the amount of work required, but they can reduce the force needed by increasing the distance over which you apply it.

The six types of simple machines are: inclined plane, wedge, screw, lever, wheel and axle, and pulley.

Mechanical advantage (MA) measures how much a simple machine multiplies your force:

$$\text{MA} = \frac{\text{output force}}{\text{input force}}$$

An MA greater than 1 means the machine multiplies your force. A ramp with MA = 3 means you apply only one-third of the force you would need without it.

# Quick Reference: Combined Vocabulary

The table below brings together the most important terms from all three lessons at a glance.

| Term | Definition | Lesson | |---|---|---| | Motion | A change in position relative to a reference point | L1 | | Reference point | Fixed location used to describe position or motion | L1 | | Speed | Distance traveled per unit of time (s = d/t) | L1 | | Velocity | Speed plus direction | L1 | | Instantaneous speed | Speed at one specific moment | L1 | | Average speed | Total distance ÷ total time | L1 | | Position-time graph | Graph showing position (y) vs. time (x) | L2 | | Slope | Steepness of a line on a graph; equals speed on a position-time graph | L2 | | Force | A push or pull on an object; measured in newtons (N) | L3 | | Net force | The combined result of all forces on an object | L3 | | Balanced forces | Forces with net force = 0; no change in motion | L3 | | Unbalanced forces | Forces with net force ≠ 0; motion changes | L3 | | Inertia | An object's tendency to resist changes in motion | L3 | | Newton's 1st Law | Objects keep their motion unless an unbalanced force acts | L3 | | Newton's 2nd Law | F = ma; acceleration depends on force and mass | L3 | | Newton's 3rd Law | Every action has an equal and opposite reaction | L3 | | Kinetic energy | Energy of motion | L4 | | Potential energy | Stored energy (height, position, or condition) | L4 | | Work | Force × distance (W = F × d); measured in joules (J) | L4 | | Simple machine | Device that changes the direction or size of a force | L4 | | Mechanical advantage | Output force ÷ input force; how much a machine multiplies force | L4 |