motion: 8.2
DESCRIPTION
Motion: 8.2. THURSDAY APRIL 17 th Cheetah clip. 8.2 Average Velocity. You will learn the difference between speed and velocity and how to use position-time graphs to calculate average velocity. Questions. What is speed? What is velocity? What is the difference between them?. - PowerPoint PPT PresentationTRANSCRIPT
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Motion: 8.2
•THURSDAY APRIL 17th
•Cheetah clip
(c) McGraw Hill Ryerson 2007
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8.2 Average Velocity
•You will learn the difference between speed and velocity and how to use position-time graphs to calculate average velocity.
(c) McGraw Hill Ryerson 2007
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Questions
•What is speed?•What is velocity?•What is the difference between
them?
(c) McGraw Hill Ryerson 2007
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(c) McGraw Hill Ryerson 2007
The need for speed.
• Speed ( ) is the distance an object travels during a given time interval divided by the time interval. Speed is a scalar quantity. The SI unit for speed is metres per second (m/s).
See pages 362 - 363
v
v
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Remember this slide from 8.1
•Scalar•Distance - d
SI unit: metres
•Time – tSI unit - s
•Speed – SI unit – m/s
•Vector•Position -
SI unit: metres
•Displacement –SI unit – metres (m)
(c) McGraw Hill Ryerson 2007
d
∆d
ح
v
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What is velocity?
•Velocity ( ) is the displacement of an object during a time interval divided by the time interval.
Velocity describes how fast an object’s position is changing.
(c) McGraw Hill Ryerson 2007
v
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Velocity
•Velocity is a vector quantity and must include direction.The direction of the velocity is the same as the
direction of the displacement.
•The SI unit for velocity is metres per second (m/s).
(c) McGraw Hill Ryerson 2007
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Remember this slide from 8.1
•Scalar•Distance - d
SI unit: metres
•Time – tSI unit - s
•Speed – SI unit – m/s
•Vector•Position -
SI unit: metres
•Displacement –• SI unit – metres (m)
•Velocity – SI unit – m/s
(c) McGraw Hill Ryerson 2007
d
∆d
ح
v v
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Same Speed, different Velocities
(c) McGraw Hill Ryerson 2007
• These two ski gondolas have the same speed but have different velocities.
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Question
•But why do the two gondolas have different velocities?
(c) McGraw Hill Ryerson 2007
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Lets look at the definitions again.
•Speed ( ) is the distance an object travels during a given time interval divided by the time interval.
•Velocity ( )is the displacement of an object during a time interval divided by the time interval.
(c) McGraw Hill Ryerson 2007
v
v
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Remember the definitions of distance and displacement!
•Distance (d) is a scalar quantity that describes the length of a path between two points or locations.
•Displacement describes the straight-line distance and direction from one point to another.
(c) McGraw Hill Ryerson 2007
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Here we see the difference
(c) McGraw Hill Ryerson 2007
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Therefore:
•The two gondolas are travelling at the same speed.
•But they are traveling in opposite directions•One of the two directions must be given a
negative sign•Therefore, they have different velocities•Clip
(c) McGraw Hill Ryerson 2007
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Calculating the slope of a position-time graph
•Dash and a Cheetah are seen in a race below (motion diagram).
•Each is running at a constant velocity.
(c) McGraw Hill Ryerson 2007
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• During equal time intervals, the position of Dash changes more than the position of the Cheetah.
• Since, Dash’s displacement for equal time intervals is greater than the Cheetahs
• Dash is running faster than the Cheetah.(c) McGraw Hill Ryerson 2007
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Question
•How can we calculate how fast Dash and the Cheetah are moving?
(c) McGraw Hill Ryerson 2007
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•We need to know the displacement and the time interval.
•The motion diagram can be placed on a position-time graph.Which represents the motion of objectsWe can determine the velocity of the objects
from the graph
(c) McGraw Hill Ryerson 2007
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• Does Dash or the Cheetah’s motion have the greater slope?
• Which one is running faster?
(c) McGraw Hill Ryerson 2007
Dash
Cheetah
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(c) McGraw Hill Ryerson 2007
Calculating the Slope of the Position-Time Graph
•The slope of a graph is represented by rise/run.•This slope represents the change in the y-axis
divided by the change in the x-axis.
Dash
Cheetah
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Calculating the Slope of the Position-Time Graph
•On a position-time graph the slope is the change in position (displacement) ( ) divided by the change in time ( ).
•The steeper the slope the greater the change in displacement during the same time interval.
(c) McGraw Hill Ryerson 2007
slope d
t
t
d
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(c) McGraw Hill Ryerson 2007
Dash
Cheetah
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Lets calculate and compare the slopes of Dash and the Cheetah.
• Slope =
= 2.0 m/s foreword
(c) McGraw Hill Ryerson 2007
Dash Cheetah
d t
d t
• Slope =
= 4.0 m/s foreword
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Average Velocity
•Compare the two slopes:Dash – 4.0 m/sSonic – 2.0 m/s
• Is the slope related to the runners speed based on this information?
(c) McGraw Hill Ryerson 2007
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Lets find out.
•Look at the units m/s•The slope shows on average how many
metres Dash and the Cheetah moved in 1 second
•Therefore, the slope of a position-time graph for an object is the object’s average velocity.
(c) McGraw Hill Ryerson 2007
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(c) McGraw Hill Ryerson 2007
Average Velocity
•Average velocity is the rate of change in position for a time interval.
•The symbol of average velocity is:•Average velocity is a vector and includes a
direction.
See pages 365 - 366
v av
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Question
•Do you remember what type of slopes a position-time graph can contain?PositiveZeroNegative
(c) McGraw Hill Ryerson 2007
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Position-time graphs and average velocity
On a position-time graph, if forward is given a positive direction:A positive slope means that the object’s
average velocity is forward.
(c) McGraw Hill Ryerson 2007
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Position-time graphs and average velocity
•On a position-time graph, if forward is given a positive direction:
• Zero slope means the object’s average velocity is zero.
(c) McGraw Hill Ryerson 2007
Which means the object is stationary!
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Position-time graphs and average velocity
•On a position-time graph, if forward is given a positive direction:A negative slope means that the object’s
average velocity is backward.
(c) McGraw Hill Ryerson 2007
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Review
(c) McGraw Hill Ryerson 2007
Time Interval t1- 0 t2 –t1 t3 – t2
Velocity
Motion Returning to the origin at a uniform speed.
Moving away from the origin at a uniform speed
NegativezeroPositive
Remaining stationary
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Note:
•Since the slope of a position-time graph is the average velocity we can use this relationship to calculate the average velocity without analyzing a position-time graph.
(c) McGraw Hill Ryerson 2007
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(c) McGraw Hill Ryerson 2007
Calculating Average Velocity
The relationship between average velocity, displacement, and time is given by:
Use the above equation to answer the following questions.1. What is the average velocity of a dog that takes 4.0 s to run
forward 14 m?
1. A boat travels 280 m east in a time of 120 s. What is the boat’s average velocity?
See page 368
v av
d
t
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•More to come tomorrow.
(c) McGraw Hill Ryerson 2007
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Finishing off 8.2
•TUESDAY APRIL 22nd
•Clip
(c) McGraw Hill Ryerson 2007
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(c) McGraw Hill Ryerson 2007
Remember from last day
•Average velocity is the rate of change in position for a time interval.
•The symbol of average velocity is:•Average velocity is a vector and includes a
direction.
See pages 365 - 366
v av
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Remember
•The relationship between average velocity, displacement, and time is given by:
•So we can rearrange this equation to find displacement.
(c) McGraw Hill Ryerson 2007
v av
d
t
d
v av t
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Question
•What is displacement?•Displacement describes the
straight-line distance and direction from one point to another.
(c) McGraw Hill Ryerson 2007
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(c) McGraw Hill Ryerson 2007
Calculating Displacement
The relationship between displacement, average velocity, and time is given by:
See page 369
d
v av t
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Use the above equation to answer the following questions.
1. What is the displacement of a bicycle that travels 8.0 m/s [N] for 15 s?
2. A person, originally at the starting line, runs west at 6.5 m/s. What is the runner’s displacement after 12 s?
(c) McGraw Hill Ryerson 2007
d
v av t
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Finding time!
•To find time, the equation can be rewritten again.
•So, from
•We can now write the above
(c) McGraw Hill Ryerson 2007
d
v av t
t d
v av
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(c) McGraw Hill Ryerson 2007
Calculating Time
The relationship between time, average velocity, and displacement is given by:
See page 369
t d
v av
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Use the above equation to answer the following questions.
1. How long would it take a cat walking north at 0.80 m/s to travel 12 m north?
2. A car is driving forward at 15 m/s. How long would it take this car to pass through an intersection that is 11 m long?
(c) McGraw Hill Ryerson 2007
15 s
0.73 s
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Converting between m/s and km/h
•How would you convert velocity in km/h to m/s?1. Change kilometres to metres:
1000m = 1 km or 1 km = 1000 m
2. Hours to seconds:
3600 s = 1 h or 1 h = 3600 s
(c) McGraw Hill Ryerson 2007
Speed zone limits are stated in kilometres per hour (km/h).
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(c) McGraw Hill Ryerson 2007
Converting between m/s and km/h
• Multiply by 1000 and divide by 3600
or• Divide the speed in km/h by 3.6 to
obtain the speed in m/s.
See page 369
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Example:
•For example, convert 75 km/h to m/s.
(c) McGraw Hill Ryerson 2007
75 km
1h
1000m
1km
1h
3600s
21m/s
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Example
•55 km/h [W]?
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= 15 m/s [W]
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(c) McGraw Hill Ryerson 2007
Try the following unit conversion problems.
1. Convert 95 km/h to m/s.
2. A truck’s displacement is 45 km north after driving for 1.3 h. What was the truck’s average velocity in km/h and m/s?
3. What is the displacement of an
airplane flying 480 km/h [E]
during a 5.0 min time interval? See page 369
26 m/s
35 km/h [N], 9.6 m/s [N]
40 km [E] or 40, 000 m [E]
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•End of Chapter 8
(c) McGraw Hill Ryerson 2007