Scalar Quantities O Scalar is quantities (amounts) that are fully described by a magnitude (or numerical value) alone. Magnitude= The size of an object; no direction A has a greater magnitude than B

Examples of Scalar O 68 degrees Fahrenheit O $37.50 O 35 mph O 7000 ft Graphical representations will be discussed later.

Vector Quantities O A Vector is something that has two and only two defining characteristics: 1. Magnitude : the meaning of magnitude is 'size' or 'quantity‘ 2. Direction: the meaning of direction is quite self-explanatory. It simply means that the vector is directed from one place to another.

Examples of Vector O 35 mph EAST O 7000 feet NORTH O 20 miles NORTHEAST Graphical representations of these will be discussed later.

Distance O Distance is the magnitude between two interval points. (Scalar Quantity) Distance= Sum of total movement Chris walked 200 yards to Cherry’s house. He left Cherry’s house and walked 50 yards to the store. After leaving the store he walked to same path home. What was the total distance traveled by Chris?

Displacement Displacement= the change in position of an object. (Vector Quantity) Δ x = x f – x i Chris walked 200 yards to Cherry’s house. He left Cherry’s house and walked 50 yards to the store. After leaving the store he walked to same path home. What was Chris’ total displacement?

Prompt O Explain the difference between distance and displacement. Provide Examples O Explain the difference between scalar and vector. Provide Examples. Answer in complete sentences.

Complete this problem. Steven wakes up every morning to run. He runs up the street 12 blocks (north). He turns around runs 8 blocks (south) to a local store to pick up his morning sausage and biscuit. While he eats, calculate his displacement and distance up to the store. *Remember which one is scalar and which one is vector.

Positive and Negative Displacement

Positive Displacement

Negative Displacement

Wait I thought displacement was a vector quantity! Correct. Although a sign is sufficient when directions are not given. For example: -4 meters is a vector representation

Example Is this positive or negative displacement?

Prompt O Explain the circumstances surrounding a positive or negative displacement.

Speed O Speed is the amount of distance covered over a certain period of time. (Scalar) Speed = distance time

Velocity O Velocity is the rate at which an object changes (displacement) position over a period of time. (Vector) Velocity= displacement or time Average Velocity = Δ x = x f -x i Δ t t f -t i

Example Velocity= 2 ft/sec east

Let’s look at an example problem Trey runs the 400 m race in seconds. What was his average velocity? V avg = Δ Displacement Δ Time (400-0) = +8.1 m/s ( )

Let’s look at another example O Laquisha’s average velocity as she drove to the store was 12 miles per hour (Lots of traffic). It took her 20 minutes to reach the store. How much distance did she travel. 20 min. X 1 hour = 20/60= 0.33 hours 60 min. 12 mph= Displacement = 3.96 miles 0.33 hours

Prompt O Explain the difference between speed and velocity. Provide examples O I did not provide a definition for average velocity. Just by examining the formula, provide a good definition.

O Create a line graph to represent the data given. Time (x)Position (y)

What can this graph tell us?

Chart Exercise O Using the chart complete the following: Example: What is the slope between 0-3 seconds? Slope= yf-yi = 9-0 = 9/3 or 3 xf-xi 3-0 2) 2-4 seconds 3) 3-6 4) 0-6

Guess what? O You have actually found multiple average velocities. O So, for your example the average velocity was +3 m/s

What else can this graph tell us?

Chart exercise This time find slope at individual points. Example: 3 seconds Slope= y/x 9/3 or 3 m/s 1) 2 2) 4 3) 5 4) 0

Instantaneous Velocity O You just calculated instantaneous velocity. The example given illustrates that at 3 seconds the instant velocity was +3 m/s What is going on between 3 & 4? What would it mean if the line between two time periods looked liked this “ “