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)
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 = initial position
d2 = final position
Δd = displacement
d1
d2
Δd
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.
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:
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
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!):
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
5
6
7
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:
-7
-6
-5
-4
-3
-2
-1
0
1
Meters
4.
5.
6.
7.
Put an “s” at the 2 m mark.
Put a “d” at the -6 m mark.
Put a “k” at the 7 m mark.
Put an “e” at the –1 m mark.
2
3
4
C. Changing positions:
Objects often change positions. In this activity, find the initial and final positions of objects.
final
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
initial
4
5
6
7
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
10 meters
25 meters
A.
B.
C.
D.
What distance does Bessie the cow travel? 25 meters
What distance does Sally the bird travel? 10 meters
What is Bessie the cow’s displacement? 10 meters
What is Sally the bird’s displacement? 10 meters
B
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
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
final
initial
9 A bike moving along a number line, from a position of 4 m to –3m
final
-7
-6
-5
-4
-3
-2
initial
-1
0
1
2
3
4
5
6
7
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.)
xf
xi
-7
-6
-5
-4
-3
-2
-1
0
1
Meters
2
3
4
5
6
7
14. Draw an arrow showing an object that moves from the –4 m position to the 5 m position.
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
Meters
15. Draw an arrow showing an object that moves from the 7 m position to the 1 m position.
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
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
xi
xf
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
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
xi
xf
-7
-6
-5
-4
-3
-2
-1
0
1
Meters
2
3
4
5
6
7
™ The following shows a displacement of +3 m
xf
xi
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
3
4
5
6
7
Meters
™ The following shows a displacement of +4 m
xf
xi
-7
-6
-5
-4
-3
-2
-1
0
1
2
Meters
Use the number line below to answer the following questions:
xi
-7
-6
-5
-4
-3
xf
-2
-1
0
1
2
3
4
5
6
7
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:
xf
xi
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
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 -)]? ____________________
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
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
i.
Is Freddy’s total displacement equal in size to Freddy’s total distance traveled?
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:
 _______________________________________________________
 _______________________________________________________
Velocity (symbol _______________)
 VELOCITY is a measure of the ___________________________________________________________
________________________________________________.
 Units are ____________________, OR _______________________________.
 EQUATION:
 where:



_____ ________________________________
_____________________________________
_____ ________________________________
d1
d2
Δd
What was the average speed?
 _______________________
 _______________________
 _______________________
 _______________________
 _______________________
 _______________________
 _______________________
_______________________
What was the average velocity?
 _______________________
 _______________________
 _______________________
 ______________________________________________
 _______________________
 _______________________
 _______________________
 _____________________________________________________________________
 _______________________
HOMEWORK
 Complete the following sheets.
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?
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?
REARRANGING EQUATIONS
 POINTS to REMEMBER:
 ______________________________________________________________________________________
_____________________________________________________________________________________.
 _____________________________________________________________________________________.
 ______________________________________________________________________________________
_____________________________________________________________________________________.
 Rearrange the following equations to solve for the variable indicated:

t

𝑎=
𝑣
𝑡
y = mx + b
Solve for v.
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.”
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!!!