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 FahrenheitO $37.50O 35 mphO 7000 ft

Graphical representations will be discussed later.

Vector QuantitiesO 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 VectorO 35 mph EASTO 7000 feet NORTHO 20 miles NORTHEAST

Graphical representations of these will be discussed later.

DistanceO 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?

DisplacementDisplacement= the change in position of an object. (Vector Quantity)

Δx = xf – xi

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?

PromptO 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?

PromptO Explain the circumstances

surrounding a positive or negative displacement.

SpeedO Speed is the amount of distance

covered over a certain period of time. (Scalar)

Speed = distance time

VelocityO Velocity is the rate at which an object

changes (displacement) position over a period of time. (Vector)

Velocity= displacement or

time

Average Velocity = Δx = xf-xi Δt tf-ti

Example

Velocity= 2 ft/sec east

Let’s look at an example problem

Trey runs the 400 m race in 49.45 seconds. What was his average velocity?

Vavg = ΔDisplacement ΔTime

(400-0) = +8.1 m/s (49.45-0)

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

PromptO 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)

0 01 32 63 94 45 76 10

What can this graph tell us?

Chart ExerciseO 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 3-02) 2-4 seconds3) 3-64) 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 secondsSlope= y/x 9/3 or 3 m/s

1)22)43)54)0

Instantaneous VelocityO 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 “ “