Motion: 8.2 THURSDAY APRIL 17 th Cheetah clip (c) McGraw Hill Ryerson 2007

Motion: 8.2

•THURSDAY APRIL 17th

•Cheetah clip

(c) McGraw Hill Ryerson 2007

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?



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

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)


d

∆d

ح

v

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.


v

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).


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


d

∆d

ح

v v

Same Speed, different Velocities


• These two ski gondolas have the same speed but have different velocities.

Question

•But why do the two gondolas have different velocities?


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.


v

v

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.


Here we see the difference


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


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.


• 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

Question

•How can we calculate how fast Dash and the Cheetah are moving?


•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


• Does Dash or the Cheetah’s motion have the greater slope?

• Which one is running faster?


Dash

Cheetah


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

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.


slope d

t

t

d


Dash

Cheetah

Lets calculate and compare the slopes of Dash and the Cheetah.

• Slope =

= 2.0 m/s foreword


Dash Cheetah

d t

d t

• Slope =

= 4.0 m/s foreword

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?


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.



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

Question

•Do you remember what type of slopes a position-time graph can contain?PositiveZeroNegative


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.



•On a position-time graph, if forward is given a positive direction:

• Zero slope means the object’s average velocity is zero.


Which means the object is stationary!


•On a position-time graph, if forward is given a positive direction:A negative slope means that the object’s

average velocity is backward.


Review


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

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.



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

•More to come tomorrow.


Finishing off 8.2

•TUESDAY APRIL 22nd

•Clip



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

Remember

•The relationship between average velocity, displacement, and time is given by:

•So we can rearrange this equation to find displacement.


v av

d

t

d

v av t

Question

•What is displacement?•Displacement describes the

straight-line distance and direction from one point to another.



Calculating Displacement

The relationship between displacement, average velocity, and time is given by:

See page 369

d

v av t

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?


d

v av t

Finding time!

•To find time, the equation can be rewritten again.

•So, from

•We can now write the above


d

v av t

t d

v av


Calculating Time

The relationship between time, average velocity, and displacement is given by:

See page 369

t d

v av

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?


15 s

0.73 s

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


Speed zone limits are stated in kilometres per hour (km/h).


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

Example:

•For example, convert 75 km/h to m/s.


75 km

1h

1000m

1km

1h

3600s

21m/s

Example

•55 km/h [W]?


= 15 m/s [W]


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]

•End of Chapter 8


Documents

Motion: 8.2 THURSDAY APRIL 17 th Cheetah clip (c) McGraw Hill Ryerson 2007