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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 “ “