Describing Motion: Position, Speed, Velocity, and Average Velocity (Lesson 1)

What it is: Where an object is located, measured by how far it is and in what direction from a starting point.
Starting Point (Reference Point): A fixed object or place you use to tell where other things are. Like using your car to find a friend's car.
Imagine a Number Line: Think of the starting point as 0. Things in one direction are positive numbers, and things in the opposite are negative.
Distance vs. Direction: Distance tells you how far. Direction tells you which way (e.g., in front or behind).
Ways to Measure Distance: We use "car-lengths" in driving, but mostly it's meters (m).
Positive and Negative: A positive number means one direction (e.g., forward or east), a negative number means the opposite direction (e.g., backward or west).
- Example: A red car is +15 m from your black car (it's 15 m in front). A white van is -21 m from your black car (it's 21 m behind).
- Another Example: If the front of your black car is the starting point, the red car's front is 15 m away, and the white van's front is -21 m away.
- Picture It: Draw a line with 0 at your starting point. Negative numbers are behind, positive numbers are in front.

How to do it: Always state both how far and in what direction from your chosen starting point.
Remember the Number Line: The starting point is 0. Distances going one way are positive, and the other way are negative.
Quick Way to Write It:
- White van is -21 m from the black car.
- Red car is +15 m from the black car.
Main Idea: Use the starting point to explain how far and in which direction another object sits.

Question: If the front of the red car is your new starting point, how far away is the white van?

Speed: How quickly an object moves; it's the distance it covers in a certain amount of time.
- Rate (what it means): How much of something happens per unit of something else. Like how many hot dogs eaten per minute.
- Example: Someone eats 60 hot dogs in 10 minutes. Their eating rate is \frac{60}{10} = 6 hot dogs per minute.
- Example: Watermelon costs 0.70 per pound.
- Speed Units: Always distance divided by time, like kilometers per hour (km/h) or meters per second (m/s).
- Look at This: The same speed can be shown in different ways:
- 3 m in 1 s means 3 m/s
- 6 m in 2 s also means 3 m/s
- 12 m in 4 s also means 3 m/s
Velocity: This is speed plus the direction it's moving. It has both a size (the speed) and a direction.
- Velocity Units/Examples: A car's velocity might be "km/h in a specific direction," or a runner's is "4 m/s toward the finish line," a snail's is "1.5 cm/min to the east."
- Changing Velocity: Velocity can change. To describe motion over a period, we use average velocity.

What it is: The total change in an object's position (displacement) divided by the time it took.
Formula:
- \bar{v} = \frac{\text{change in position}}{\text{time taken}} = \frac{\text{final position} - \text{start position}}{\text{time taken}}
Example (Figure 2B): A yellow car moves from a starting point of -70 m to an ending point of 20 m in 3 seconds.
- Change in Position: 20 - (-70) = 90\,\text{m} (It moved 90 m total).
- Average velocity: \bar{v} = \frac{90\,\text{m}}{3\,\text{s}} = 30\,\text{m/s}
- Direction: East (because it's the positive direction on our number line).
Velocity and Direction:
- If an object moves in the positive direction, its velocity is positive (e.g., 30 m/s east).
- If an object moves in the negative direction, its velocity is negative (e.g., 25 m/s west).
With Signs:
- Red car: velocity is 25\,\text{m/s} west (negative direction).
- Yellow car: velocity is 30\,\text{m/s} east (positive direction).
Important: To fully describe velocity, you need to say both the speed and the direction.

The plus (+) or minus (-) sign on velocity simply tells you the direction of movement along your chosen path.
Example: If a car moves from a start of 50\,\text{m} to an end of -25\,\text{m} in 3 seconds, then:
- Change in position: -25 - 50 = -75\,\text{m}
- Average velocity: \bar{v} = \frac{-75\,\text{m}}{3\,\text{s}} = -25\,\text{m/s}, which means 25 m/s to the west.
This shows that if you move towards the negative side of your number line, you'll get a negative average velocity.

How do you figure out an object's average velocity?
- Answer: Use the formula: \bar{v} = \frac{\text{final position} - \text{start position}}{\text{time taken}}

Perspective Matters: Position, speed, and velocity always depend on your chosen starting point or direction.
Everyday Use: Knowing these concepts helps with driving safely, navigating, and understanding how things move around us every day.
Safety First: Accurate measurements of where things are and how fast they're going are crucial for driving safety and understanding motion.

Change in Position (Displacement): \Delta x = \text{final position} - \text{start position}
Time Taken: \Delta t (or just t if you start counting from zero)
Average Velocity: \bar{v} = \frac{\text{change in position}}{\text{time taken}} = \frac{\text{final position} - \text{start position}}{\text{time taken}}
Speed: \text{speed} = \frac{\text{distance}}{\text{time}}
Velocity (with direction): Speed plus a specific direction (e.g., \bar{v} = 30\,\text{m/s east}$$)