SCALAR VS. VECTOR QUANTITIES

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SCIENCE 1206 – MOTION - Unit 3 Slideshow 2 – SPEED CALCULATIONS NAME:__________________  TOPICS OUTLINE  SCALAR VS. VECTOR  SCALAR QUANTITIES  DISTANCE  TYPES OF SPEED  SPEED CALCULATIONS  DISTANCE-TIME GRAPHS  SPEED-TIME GRAPHS

SCALAR VS. VECTOR QUANTITIES SCALAR QUANTITIES

 Any quantity that has _____________________________________________, but ___________________________________.  EXAMPLES:  ______________________________________________  ______________________________________________  ______________________________________________  ______________________________________________ VECTOR QUANTITIES

 Any quantity that has ______________________________________________, and _____________________________________.

 Direction is symbolized by

_________________________________________________________________________.  Ex: velocity has the symbol ____________

 EXAMPLES:

 ______________________________________________  ______________________________________________  ______________________________________________

Position, Displacement & Distance

 Distances and directions are generally stated relative to a ___________________________________.  The reference point is usually _____________________________________________. If you begin a trip

from home, then home is your reference point.

 Specifying where you are or where you are going requires you to indicate the direction. In writing , ___________________________________________________________________________.

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Position

 Your position is the _________________________________________________ from a reference point.  You could be ______________________________________ of a reference point.

 Note: The direction is given in ________________________________, and usually a compass direction or a right/left or forward/backward direction.

 A quantity that involves a direction, such as position, is called a ________________________________.  A vector quantity has ___________________________________________________________________.

For example: ______________________________________________

 A quantity that involves only size, but no direction, is called a __________________________________.  Mass is a scalar quantity. _________________________ has no direction associated with it.

 Vector quantities are represented by symbols that include ____________________________________ ________________________; scalar quantities ___________________ have the arrow over the symbol.

Scalar quantity  Distance ____________________________________________  Time ____________________________________________ Vector quantity  Position ____________________________________________  Displacement ____________________________________________

 On a straight line, such as a track or a street, position, d, is sometimes stated as positive or negative relative to a zero point.

 These positions can be shown on a diagram.

d₁

d2

d1= initial position d2= final position

Δd = displacement

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DISPLACEMENT

 Displacement is defined as ___________________________________________________________.  The symbol for displacement , Δd, includes the symbols Δ (___________________________________

________) and d (__________________________________ _______________).

 Our person goes from the bus stop to the music store, then to the shoe store. Δd = _____________________________________________

_____________________________________________

__________________________________________________________________

 What is the distance traveled (bus stop to music store to shoe store)? Δd = _____________________________________________

_____________________________________________ Position, Displacement & Distance

 Distance is a measure of the __________________________________________________________ _________________________________________.

 Units are _________________________________, OR ______________________________________.  _____________________________________________

HOMEWORK

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Name:____________________________ Block:_____ Date:_____/_____/_____

Introduction to Position, Distance, and Displacement

A. Reading Positions:

When objects start moving, it is useful to be able to describe an object’s location.

To describe location, imagine a meterstick is placed next to the object. The meterstick acts like a number line.

9 Objects to the right of the zero (0) have positive positions 9 Objects to the left of the zero (0) have negative positions Examples:

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Meters

A. What is the position of the lightning bolt? 5 meters

B. What is the position of the happy face? 1 meters

C. What is the position of the sun? -4 meters

Use the number line below to give the positions of the objects (Don’t forget units!):

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Meters

1. What is the position of the heart? _______________________ 2. What is the position of the diamond? _______________________ 3. What is the position of the cross? _______________________

B. Locating Positions:

Draw the object at the indicated locations:

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Meters 4. Put an “s” at the 2 m mark.

5. Put a “d” at the -6 m mark. 6. Put a “k” at the 7 m mark. 7. Put an “e” at the –1 m mark.

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C. Changing positions:

Objects often change positions. In this activity, find the initial and final positions of objects.

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Meters

8. What is the initial position of the frog? _______________________ 9. What is the final position of the frog? _______________________

10. If the frog traveled in a straight line from the initial position to the final position, what distance did it travel? _______________________

D. Distance and Displacement:

Now we will learn about two words that seem similar, but have different meanings in physics. Distance: measurement of the actual path traveled

Displacement: the straight-line distance between 2 points

¾ If an object travels in one direction in a straight line, distance traveled is EQUAL to the displacement.

¾ Often, objects do not travel in straight lines (or they move back and forth), so distance and displacement are NOT EQUAL.

Examples:

Bessie the cow and Sally the bird both traveled from point “A” to point “B.” Sally traveled in a straight line and Bessie did not.

A. What distance does Bessie the cow travel? 25 meters

B. What distance does Sally the bird travel? 10 meters

C. What is Bessie the cow’s displacement? 10 meters

D. What is Sally the bird’s displacement? 10 meters

initial final A B 10 meters 25 meters

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11. If the car travels once around the racetrack, what distance does it travel? _______________ 12. If the car travels twice around the racetrack, what distance does it travel? ______________ 13. If the car travels once around the racetrack, what is its displacement? _________________

E. Showing Displacement:

When an object moves, an arrow can be drawn to show the displacement The arrow points in the direction of motion

9 The arrow should start (non-arrow side) at the starting position and end (arrow side) at the ending position

9 The arrow should be straight Examples:

9 A school bus

9 A bike moving along a number line, from a position of 4 m to –3m

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Meters

9 Any object, using “xi“ to represent the initial position and “xf“ to represent

the final position. (In this case, the object moves from the –6 m position to the 3 meter position.)

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Meters

the track is 100 meters around initial final initial final xi xf

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14. Draw an arrow showing an object that moves from the –4 m position to the 5 m position.

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Meters

15. Draw an arrow showing an object that moves from the 7 m position to the 1 m position.

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Meters

F. What about direction?:

Displacement also includes direction! Possible directions include:

9 positive or negative 9 left or right

9 up or down

9 north, south, east, or west

In this class, we will often use positive and negative to show direction. 9 A displacement is negative if the arrow points to the left or down 9 A displacement is positive if the arrow points to the right or up

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Meters

16. Is the above displacement positive or negative? ____________________

G. Calculating Displacement:

Remember: Displacement is the straight-line distance between 2 points. To give a displacement we should give both the size and the direction.

To find the size of the displacement, count the number of spaces from the initial to the final position.

The following shows a displacement of –5 m

-6 -7 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 Meters xi xf xi xf

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The following shows a displacement of +3 m

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Meters

The following shows a displacement of +4 m

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Meters

Use the number line below to answer the following questions:

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Meters 17. Draw an arrow to show the displacement.

18. Is the initial position positive or negative? ____________________ 19. Is the final position positive or negative? ____________________ 20. Is the displacement positive or negative? ____________________

21. What is the displacement [size (with units) and direction (+ or -)]? ____________________

Use the number line below to answer the following questions:

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Meters 22. Draw an arrow to show the displacement.

23. Is the initial position positive or negative? ____________________ 24. Is the final position positive or negative? ____________________ 25. Is the displacement positive or negative? ____________________

26. What is the displacement [size (with units) and direction (+ or -)]? ____________________

xi xf

xi

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Meters

27. Use the above number line to help answer the following question: Freddy the cat started at the –3 meter position. He then walked to other locations. Mark each new location with the letter for that part.

a. Freddy started at the –3 m position. (mark this position with an “a”)

b. First, Freddy walked 2 meters in the positive direction (right) to the –1 m position. c. Second, Freddy walked 5 meters in the positive direction to the +4 m position. d. Third, Freddy walked 1 meter in the negative direction to the +3 m position. e. Finally, Freddy walked 8 meters in the negative direction to the –5 m position. f. Draw a displacement arrow that starts at Freddy’s initial position (-3 m) and ends

at Freddy’s final position (-5 m).

g. What was Freddy’s total displacement? (for this, you only need to look at his initial and final position) (be sure to include sign, number, and units)

____________________

h. To get the distance Freddy traveled, add up all the distances: 2m + 5m + 1m + 8m = ______________ meters

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TIME (symbol ______________)

 TIME is measured as the __________________________________________________________________.  Units are ______________________________, OR _____________________________.  ______________________________________  EQUATION:  where:  Δt = _______________________________  t2 = ________________________________  t1 = ________________________________ SPEED (symbol ______________)

 SPEED is a measure of the ________________________________________________________________.  Units are _______________, OR _______________.  _______________________________________  EQUATION:  where:  Δv = _______________________________  Δd= ________________________________  Δt= ________________________________

THREE TYPES OF SPEED 1. CONSTANT SPEED (Δv)

 AKA ______________________________________

 When an object is travelling at constant speed, it is travelling at the

_____________________________________________________________________.  EXAMPLE  _______________________________________________________  _______________________________________________________ 2. AVERAGE SPEED (vav)  A measure of the __________________________________________________________________. 3. INSTANTANEOUS SPEED (vinst)

 A measure of the __________________________________________________________________.  Instantaneous speed is ________________________________ by an object’s PREVIOUS SPEED or

HOW LONG is has been moving.  EXAMPLE:

 _______________________________________________________  _______________________________________________________

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Velocity (symbol _______________)

 VELOCITY is a measure of the ___________________________________________________________ ________________________________________________.  Units are ____________________, OR _______________________________.  EQUATION:  where:  _____ ________________________________  _____________________________________  _____ ________________________________

What was the average speed?  _______________________  _______________________  _______________________  _______________________ _______________________  _______________________  _______________________  _______________________

d

₁

d

₂

Δd

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What was the average velocity?  _______________________  _______________________  _______________________  ______________________________________________  _______________________  _______________________  _______________________  _____________________________________________________________________  _______________________

HOMEWORK

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The Fun World of Position, Displacement, Speed and Velocity

Science 1206: Physics Name________________________

1. Dude the dog travels 3.5 km [E] in a 25 minute period. Calculate his velocity in: a. metres per second b. kilometres per min c. kilometres per hour

2. George the goldfish begins his day 3.5 cm [E] of the rock in his bowl. He ventures 8.0 cm [W] before traveling another 16 cm [E]. He travels this ground in 35 seconds.

a. Draw a picture of this travel.

b. What is his final position?

c. What is his velocity?

d. What is his speed?

3. A school bus is on its morning run. It begins at a position 3.0 km [E] of school, drives to a position 2.0 km [W] of school before stopping at a position 4.0 km [E] of school.

a. Draw a picture of this travel.

b. What is the final position?

c. What is the average velocity?

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4. Jason leaves his house and walks 100 m [W] over to Bart’s house. They walk 300 m [E] to Nathan’s. Together they walk 400 m [W] to the store and share a 200 g bag of chips and a 2L bottle of pop.

a. Draw and clearly label a number line for this adventure.

b. What is their final position. What have you assumed about Jason’s house?

c. What is Jason’s overall displacement? (show work)

d. What distance did Jason travel?

e. If the total time was 30 min. Calculate his average velocity in km/h and m/s.

f. Calculate his average speed in km/h and m/s.

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REARRANGING EQUATIONS  POINTS to REMEMBER:  ______________________________________________________________________________________ _____________________________________________________________________________________.  _____________________________________________________________________________________.  ______________________________________________________________________________________ _____________________________________________________________________________________.  Rearrange the following equations to solve for the variable indicated:



𝑎 =

𝑣

𝑡 Solve for v. t

 y = mx + b Solve for m.

PROBLEM-SOLVING SKILLS

 When doing physics problems, follow the following guidelines:

 ___________________________________________________________________________________  ___________________________________________________________________________________  ___________________________________________________________________________________  ___________________________________________________________________________________  ___________________________________________________________________________________ REARRANGING THE SPEED EQUATION

 Since the SPEED equation has only 3 VARIABLES, you can easily rearrange it using the following helpful “triangle.”

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SAMPLE PROBLEM 1

 _____________ wants to ride his bike from Corner Brook to Deer Lake, a distance of 45 km. If he only has 0.50 h to get there, what speed does he have to travel?

 _____________ wants to ride her bike from Corner Brook to Deer Lake, a distance of 45 km. Unlike ____________, she calculated her average speed to be 20.0 km/h. How long will it take her to get there?

 ______________ is travelling for a triathlon and ran at a speed of 15 km/h for 2.0 h. What distance has he travelled?

 On her scooter, ______________ travels 12 km in 2.5 h and then 15 km in 35.5 minutes. What is her average speed?

HOMEWORK

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