# SCALAR VS. VECTOR QUANTITIES

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1 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,. Sec 11.1 in Text (p. 414)

2 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. d 1 = initial position d 2 = final position Δd = displacement d 1 d 2 Δd

3 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 Complete the following Introduction to Position, Distance, & Displacement sheets.

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

5 C. Changing positions: Objects often change positions. In this activity, find the initial and final positions of objects. final initial 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 If an object travels in one direction in a straight line, distance traveled is EQUAL to the displacement. 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 10 meters B 25 meters 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

6 the track is 100 meters around 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 The arrow should start (non-arrow side) at the starting position and end (arrow side) at the ending position The arrow should be straight Examples: A school bus initial final A bike moving along a number line, from a position of 4 m to 3m final initial x i Any object, using x i to represent the initial position and x f to represent the final position. (In this case, the object moves from the 6 m position to the 3 meter position.) x f

7 14. Draw an arrow showing an object that moves from the 4 m position to the 5 m position. 15. Draw an arrow showing an object that moves from the 7 m position to the 1 m position. F. What about direction?: Displacement also includes direction! Possible directions include: positive or negative left or right up or down north, south, east, or west In this class, we will often use positive and negative to show direction. A displacement is negative if the arrow points to the left or down A displacement is positive if the arrow points to the right or up x f x i 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 x f x i

8 The following shows a displacement of +3 m x i x f The following shows a displacement of +4 m x i x f Use the number line below to answer the following questions: x i x f 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: x f x i 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 -)]?

9 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 i. Is Freddy s total displacement equal in size to Freddy s total distance traveled?

10 TIME (symbol ) TIME is measured as the. Units are, OR. EQUATION: where: Δt = t 2 = t 1 = 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 (v av ) A measure of the. 3. INSTANTANEOUS SPEED (v inst ) 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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12 Velocity (symbol ) VELOCITY is a measure of the. Units are, OR. EQUATION: where: d 1 d 2 Δd What was the average speed?

13 What was the average velocity? HOMEWORK Complete the following sheets.

14 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? d. What is the average speed?

15 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. g. If it takes Jason 10 minutes to reach Bart s house. Then what is Bart s velocity for the outing?

16 REARRANGING EQUATIONS POINTS to REMEMBER:... Rearrange the following equations to solve for the variable indicated: t a = v t Solve for v. 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.

17 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? SAMPLE PROBLEM 2 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? SAMPLE PROBLEM 3 is travelling for a triathlon and ran at a speed of 15 km/h for 2.0 h. What distance has he travelled? SAMPLE PROBLEM 4 On her scooter, travels 12 km in 2.5 h and then 15 km in 35.5 minutes. What is her average speed? HOMEWORK Do the 2 attached WORKSHEETS in your handout for homework!!!

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