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Distance and displacements. Causeway Bay. Wan Chai. Simon is in Causeway Bay . He needs to. 1 take a book to Mary at the exit gate of Mongkok MTR , and. 2 pass a gift to Jenny at the HKEAA in Wan Chai . Mongkok. From. To. Adult Fare. Causeway Bay. Mongkok. $10.0. Mongkok.

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slide2

Causeway Bay

Wan Chai

Simon is in Causeway Bay. He needs to

1 take a bookto Mary at the exit gate ofMongkok MTR, and

2 pass a gift to Jenny atthe HKEAA in WanChai.

Mongkok

slide3

From

To

Adult Fare

Causeway Bay

Mongkok

$10.0

Mongkok

Wan Chai

$10.0

Causeway Bay

Wan Chai

$3.8

(a) What is the minimum fare for Simon’s whole journey?

Hedoesn’t goout of the gates at Mongkok station.

warm up

From

To

Adult Fare

Causeway Bay

Mongkok

$10.0

Mongkok

Wan Chai

$10.0

Causeway Bay

Wan Chai

$3.8

Warm-up

(a) What is the minimum fare for Simon’s whole journey?

For his whole journey,

hisposition changes from CausewayBay station to Wan Chai station.

slide5

(b) Do you agree with the following statements about travelling by MTR?

Disgree

Agree

More should be paid for longer distance travelled.

Fare depends on where he passesthe exit gate only.

1 unit of length

X

North Pole

Y

1 Unit of length

Symbol:m

SI unit: metre

Old definition:

1 m was defined as 10–7 of a quadrant of the Earth.

But no need to remember

the exact value…

2 displacement and distance
2 Displacement and distance

Displacement requires :

  • Lengthof a straight line going fromthe old to the new positions

i.e. size/magnitude

  • Direction of the movement

Simulation

2 displacement and distance8
2 Displacement and distance

your home

To go to school from home...

Size = length of this arrow

your school

displacement from home to school

A displacement has

size

& direction.

2 displacement and distance9
2 Displacement and distance

your home

To go to school from home...

l1

l2

l3

your school

Distance = length of pathyou travelled

= l1 + l2 + l3

( size of displacement)

3 vectors and scalars
3 Vectors and scalars

Vector

a quantity described by its

direction

&magnitude (size)

E.g.displacement,

velocity,

force

3 vectors and scalars11
3 Vectors and scalars

A vector can be represented by an arrow.

It tells us:

direction

length = magnitude

3 vectors and scalars12
3 Vectors and scalars

To go from A to B...

path taken

start point

end point

A

B

displacement

displacement written as AB

3 vectors and scalars13
3 Vectors and scalars

Scalar

  • quantity described by its magnitude (size) only

E.g. temperature,

distance, speed,

mass, energy

4 adding displacements

N

3 km

7 km

north

4 km

4 Adding displacements

a Graphical method

A car travels 4 km north

then 3 km north.

total distance

total distance = ?

= (3 + 4) km = 7 km

total displacement = ?

total displacement

= (3 + 4) kmnorth

= 7 kmnorth

4 adding displacements15

N

1 km

north

3 km

4 km

4 Adding displacements

a Graphical method

A car travels 4 km north

then 3 km south.

total distance

total distance = ?

= (3 + 4) km = 7 km

total displacement = ?

total displacement

= (3 + 4) kmnorth

= 1 kmnorth

4 adding displacements16

N

3 km

4 km

4 Adding displacements

a Graphical method

A car travels 4 km north

then 3 km east.

total distance = ?

total distance

= (3 + 4) km = 7 km

total displacement = ?

total displacement

5 km

= 5 km37 east of north

(by measurement)

tip to tail method

‘tip’ of p joined to ‘tail’ of q

p

q

p + q

4 Adding displacement

Tip-to-tail method:

a Graphical method

4 adding displacements18

3

tan  =

4

3 km

4 km

4 Adding displacements

b Algebraic method

It is easy to adddisplacements if they are perpendicular to each other.

E.g.

d 2 = 42 + 32

d = 5 km

N

d

5 km

 = 37

example 2

70 m

Example 2

A girl cycles a circulartrack of diameter 70 m

and stops atthe starting point.

(a)Distance travelled = ?

Distance travelled

= perimeter of track

= p× 70

= 220 m

example 220

70 m

Example 2

(b) Does she change her position?

No,

it is because she goes back to the starting position.

example 3

4km

5km

Example 3

A car travels 5 km north

and 4 km east.

(a) Total distance travelled = ?

N

Total distance

= 5 + 4 = 9km

example 222

70 m

Example 2

(c) What is her displacement?

Her overall displacement = 0 m

example 323

4km

5km

Example 3

A car travels 5 km north

and 4 km east.

(b) What is the displacement?

N

size =

= 6.40 km

tan  =

  = 38.7

6.4km

Total displacement:

6.40 km 38.7° east of north

q1 a ball suspended
Q1 A ball suspended...

A ball hung by a string swings from X to Y.

What is the size of the displacement ofthe ball?

60o

1 m

A p/3 m

B 1 m

C 1 m towardsthe right

1 m

X

Y

q2 is the speed limit
Q2 Is the speed limit...

Is the speed limit a vector or a scalar?

Scalar!