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