Chapter 12 What is motion?
Describing Motion
Point of reference: An object or group of objects that is considered to be stationary
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?
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?
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.
12.1 Measuring Motion
Displacement
distance
displacement
How do we accurately communicate distance and displacement?
12.1 Measuring Motion
A scalar is a quantity that can be completely described by one value: the magnitude (size).
12.1 Measuring Motion
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
Both Mr. Rabbit and Mr. Tortoise took the same round trip, but Mr. Rabbit slept & returned later.
12.1 Measuring Motion
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
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
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
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
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
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
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
0 1 2 3 4 50
20
40
60
80
100
120
140
Distance vs. Time
Time (s)
Dis
tanc
e(m
)
Instantaneous speed
= speed at any instantInstantaneous speedThe word ‘speed’ alone
instantaneous speed
Instantaneous speed distance travelled in an extremely short time interval
Speed
Speedometer tells the car’s speed at any instant!
Instantaneous speed
Speed
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 )
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
= 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
rate of change of displacement or
a speed in a given direction.
velocity a vector quantity
direction
magnitude(speed)
Velocity is...
12.2 Velocity
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
Average velocity
Average velocity =overall distance
total time of travel
Direction of velocity = direction of overall distance
Velocity
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
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!
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?
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...
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:
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
(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
(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
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
Acceleration
When a car moves faster and faster, its speed is increasing (velocity changed).
When a car moves slower and slower,its speed is decreasing (velocity changed).
Acceleration
When a car changes direction, its velocity changes too.
Acceleration
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
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
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
Speed Graph
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
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
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!
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.
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)
The End
0 1 2 3 4 50
20
40
60
80
100
120
140
Distance vs. Time
Time (s)
Dis
tanc
e(m
)
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
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