Chapter 12 What is motion?
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Transcript of Chapter 12 What is motion?
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Chapter 12 What is motion?
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Describing Motion
Point of reference: An object or group of objects that is considered to be stationary
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Point of Reference
From the bus driver’s perspective, what is happening to the man?
From the man standing outside’s perspective, what is happening to the bus?
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From this driver’s perspective, is he standing still, moving forward or backwards?
Point of Reference
The buildings in front of him?What about the car in his rear view mirror?
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12.1 Measuring Motion
Distance – the total length that an object has travelled.
Displacement – the distance and direction from the starting point to the ending point. Path taken is not important.
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12.1 Measuring Motion
Displacement
distance
displacement
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How do we accurately communicate distance and displacement?
12.1 Measuring Motion
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A scalar is a quantity that can be completely described by one value: the magnitude (size).
12.1 Measuring Motion
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A vector has both distance and direction.
If you walk five meters east, your displacement can be represented by a 5 cm arrow pointing to the east.
12.1 Measuring Motion
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Both Mr. Rabbit and Mr. Tortoise took the same round trip, but Mr. Rabbit slept & returned later.
12.1 Measuring Motion
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Comment on their argument.
Me, as I spent less time on the
trip.
No, I travelled longer distance every
minute.
Who runs faster?
12.1 Measuring Motion
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How can we describe how fast an object moves?
E.g. A car on Jal el Dib Highway travels 90 km in 1 hour.
We say that the car travels at a speed of 90 km/h.
Speed
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Speed is a measure of how fast something moves.
Speed = distance travelled per unit of timeSpeed = distance travelled per unit of timeSI unit: m/s or km/h (for long distances)
How can we describe how fast an object moves?
Speed
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Speed
0 1 2 3 4 50
2
4
6
8
10
12
Distance vs Time
Time (s)
Dis
tan
ce (
m)
Distance vs. Time
A
B
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Average speed does not tell the variations during the journey.
On most trips, the speed at any instant is often different from the average speed.
Average speed
Speed
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and speeds up to 60 km/h for another hour.and speeds up to 60 km/h for another hour.
Average speed
Its average speed over the whole journeyoverall distance travelled
total time of travel
slows down to 0 km/h, for an hour slows down to 0 km/h, for an hour
A car travels at 50 km/h, for an hourA car travels at 50 km/h, for an hour
=
Speed
50 km + 60 km3 h
= 36.7 km/h
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0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 160
5
10
15
20
25
30
35 Distance vs. Time
A
B
Time (s)
Dis
tanc
e (m
)
Average SpeedCalculate the average speed of the car at point A and point B
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0 1 2 3 4 50
20
40
60
80
100
120
140
Distance vs. Time
Time (s)
Dis
tanc
e(m
)
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Instantaneous speed
= speed at any instantInstantaneous speedThe word ‘speed’ alone
instantaneous speed
Instantaneous speed distance travelled in an extremely short time interval
Speed
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Speedometer tells the car’s speed at any instant!
Instantaneous speed
Speed
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Q1 The world record...
= 9.53 m/s or 34.3 km/h
( 100 m )Average speed =
10.49 s
The world record of women 100-m race is 10.49 s.
What is the average speed?
(9.53 m/s x 3600 s/h = 34308 m/h = 34.3 km/h )
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A man walks from A to B at 1 km/h
A B1 km/h
2 km/h
and returns at 2 km/h.
Average speed for the whole trip = ?
Q2
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= 1.33 km/h
A B1 km / h
2 km / h
Suppose AB = 1 kmTime for whole trip =
km/h 2
km 1
km/h 1
km 1
= 1 h + 0.5 h = 1.5 h
whole journey = 2 km
Avg. speed = distance / time= 2/1.5
Q2
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rate of change of displacement or
a speed in a given direction.
velocity a vector quantity
direction
magnitude(speed)
Velocity is...
12.2 Velocity
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speed = 300 km/hdirection = west
A subway driver’s concern is speed only.
Speed with direction
A pilot’s concern is velocity (direction & speed).
speed = 90 km h–1
Velocity
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Average velocity
Average velocity =overall distance
total time of travel
Direction of velocity = direction of overall distance
Velocity
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Instantaneous velocity
The velocity at any instant is called instantaneous velocity.
If a car moves at a constant velocity...
… its average and instantaneous velocities have the same value.
Velocity
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So Who is Faster?
Rabbit – instantaneous velocity at the
beginning and end of the race
Tortoise – average velocity over the
whole race
Answer? They BOTH are!
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In an orienteering event, Maria and Karen reach their control points at the same time.
Q1 In an orienteering event...
start, 10:00 amstart, 10:00 amMaria, 10:30 amMaria, 10:30 am
Karen, 10:30 amKaren, 10:30 am
Who runs at a higher average velocity?Who runs at a higher average velocity?
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A Maria.
B Karen.
C Undetermined since their paths are unknown.
D Incomparable since they run along different directions.
Who runs at a higher average velocity?Who runs at a higher average velocity?
Q1 In an orienteering event...
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Example 1
Batroun Jounieh
Jounieh Antelias
Antelias Airport
Distance between cities/ km
Travel time btw cities/ min
Avg. speed btw cities/ km/h
30
15.4
(a)
17
(b)
16
(c)
90
55
A car travels from Batroun to the airport in Beirut. Use the formula, s=d/t to calculate a, b and c in the following table:
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Distance between cities/ km
Travel time btw cities/ min
Avg. speed btw cities/ km/h
30
15.4
(a)
17
(b)
16
(c)
90
55
(a) Antelias Airport:
Distance = avg. speed time= 55 km/h 0.267 h
= (16min/60min/h)= 0.267 h
= 14.7 km
Example 1
Batroun Jounieh
Jounieh Antelias
Antelias Airport
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(b) Jounieh Antelias:
Time = distance / avg. speed= 15.4km/90km/h
= 0.171 h=10.3min
Distance between stations / kmJourney time between stations / sAve. speed between stations / km h–1
30
15.4
(14.7)
17
(b)
16
(c)
90
55
Batroun Jounieh
Jounieh Antelias
Antelias Airport
Distance between stations / kmTravel time btw stations / min
Avg. speed btw stations / km/h
Example 1
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(c) Batroun Jounieh:
Avg. speed = distance / time= 30km/ 0.283h
= 106 km/h
Distance between stations / km
Time between stations / min
Ave. speed btw stations / km/h
30.0
15.4
(14.7)
17
(10.3)
16
(c)
90
55
= (17min/60min/h)= 0.283 h
Batroun Jounieh
Jounieh Antelias
Antelias Airport
Example 1
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Example 1
Batroun Jounieh
Jounieh Antelias
Antelias Airport
Distance between cities/ km
Travel time btw cities/ min
Avg. speed btw cities/ km/h
30
15.4
(14.7)
17
(10.3)
16
(106)
90
55
(d) What was the total average speed for the whole trip?
Avg. speed =
Total distanceTotal time
(30+15.4+14.7)km(17+10.3+16)min/60min/h60.1km
0.722h= 83.3 km/h
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Acceleration
When a car moves faster and faster, its speed is increasing (velocity changed).
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When a car moves slower and slower,its speed is decreasing (velocity changed).
Acceleration
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When a car changes direction, its velocity changes too.
Acceleration
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Acceleration measures the change in velocity
Acceleration = velocity per unit time
Acceleration = velocity per unit time
direction
speed
overall change in velocitytotal time taken
= m s–2Unit: m s–1 / s vector quantity
=
Acceleration
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If a car accelerates at 2 m/s2, what does that mean?
t = 1 sv = 2 m/s,v = 2 m/s
v = 0
t = 2 sv = 4 m/s, v = 2 m/s
v = 6 m/s, v = 2 m/s
t = 3 s
2 m
t = 0
4 m
6 m
Acceleration
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The Ferrari 348 can go from rest to 100 km/h in 5.6 s.
Acceleration
What is its avg. acceleration (in m/s2)?Avg. acceleration
=100 km/h
5.6 s(100/3.6) m/s
5.6 s=
= 4.96 m/s2
1km/h = 1000m/3600s
1km/h = 1m/3.6s
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Speed Graph
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Acceleration Graph
What is:a) The acceleration between O and A?b) The acceleration between A and B?c) The acceleration between B and C?
45s
90s
110s
25m/s
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Q1 A running student...
A running student is slowing down in front of a teacher. With reference to the sign convention,
Acceleration of student: positive / negative
Velocity of student: positive / negative
+ve
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Q2 In 2.5 s, a car speeds up...
In 2.5 s, a car speeds up from 60 km/h to 65 km/h...
…while in 2.5 s, a bicycle goes from rest to 5 km/h.
Which one has the greater acceleration?
They have the same acceleration!They have the same acceleration!
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Q3 A car is moving in a positive direction...
A car is moving in a +ve direction.
What happens if it moves under a ve acceleration?
What happens if it moves under a ve deceleration?
The car will slow down.
The car will move in +ve direction with increasing speed.
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Quantity Unit Scalar/Vector
Speed ______ _____
Velocity ______ _____
Change in velocity ______ _____
Acceleration ______ _____
Note
Unit of time: hour (h)
km/h
km/h
km/h
km/h2
scalarvectorvectorvector
Unit of distance: kilometer (km)
(or s if using small numbers)
(or m if using small numbers)
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The End
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0 1 2 3 4 50
20
40
60
80
100
120
140
Distance vs. Time
Time (s)
Dis
tanc
e(m
)
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Airport Express takes 0.35 h to go from Batroun to the Airport (34 km).
Example 1
Batroun Jounieh
Jounieh Beirut dis.
Beirut dis. Airport
Distance between stations / km
Travel time btw stations / s
Avg. speed btw stations / km/h
2.6
8.9
(a)
153
(b)
762
(c)
90
105
Complete the table.
Avg. speed =34 km/0.35 h= 97 km/h