Section 4.2 Speed And Velocity

Section 4.2 Speed and velocity

• Speed and distance • Velocity and displacement • Instantaneous speed and instantaneous velocity © Manhattan Press (H.K.) Ltd.

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4.2 Speed and velocity (SB p. 8)

Speed and distance Besides position, how can we describe objects in motion? Speed and velocity

Go to © Manhattan Press (H.K.) Ltd.

Activity 2

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4.2 Speed and velocity (SB p. 9)

Speed and distance Distance travelled Average speed = Time taken

• A scalar • Unit: m s–1 or km h–1

e.g. The world record for the men’s 100 m race is 9.78 s

l00 m

100 Average speed = = 10.22 m s–1 9.78 © Manhattan Press (H.K.) Ltd.

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4.2 Speed and velocity (SB p. 9)

Calculation of speed

Station Distance between successive stations / km Time taken / min

1→ 2

2→ 3

2.42

1.80 4.50 1.10

3

3→ 4

2

4

4→ 5

2

From (4) Tai Wai to (5) Shatin,

Distance travelled Average speed = Time taken Thinking 3

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=

1.1 km 2 min

= 9.2 m s–1 4

4.2 Speed and velocity (SB p. 10)

Class Practice 2: Refer to Fig. 4.7. (a) Complete the following table.

Station Distance between successive stations / km Time taken / min Average speed / m s−1

5→ 6

6→ 7

7→ 8

8→ 9

9→ 10→ 11→ 10 11 12

2.00 1.80 6.70 1.15 6.25 1.50 3.50 2

3

6

2

16.7 10.0 18.6 9.6

5

2

4

20.8 12.5 14.6

Ans wer

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4.2 Speed and velocity (SB p. 10)

Class Practice 2 (Cont) : (b) Find the average speed of a KCR train for the whole journey from (1) Hunghom to (12) Lo Wu. Express your answer in m s−1. Distance travelled Average speed = Ans Time taken wer

( +1.8 + 4.5 +1.1 + 2 +1.8 + 6.7 +1.15 + 6.25 +1.5 + 3.5) x103 2 . 42 = (3 + 2 + 4 + 2 + 2 + 3 + 6 + 2 + 5 + 2 + 4) x 60 = 32 7 20 m 2 100 s = 15.58 m s-1

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4.2 Speed and velocity (SB p. 11)

Velocity and displacement Velocity =

Displacement Time taken

s v= t

Unit: m s–1 , vector (direction: same as displacement) negative (−)

-70 km h © Manhattan Press (H.K.) Ltd.

positive (+)

-1

70 km h-1 7

4.2 Speed and velocity (SB p. 11)

Velocity and displacement constant speed ≠ constant velocity • Speed = 20 km h−1 • Velocity is changing (direction changing)

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4.2 Speed and velocity (SB p. 12)

Example 2: Edmond is swimming in a 50 m long swimming pool. He takes 25 s to swim from A to B and another 30 s for the return trip. Find his average speed and his average velocity during the whole trip. Solut ion During the whole trip, distance travelled = 50 + 50 = 100 m. Distance travelled 100 Average speed = = = 1.82 m s -1 ( 25 + 30) Time taken Since the initial and final positions are the same, displacement = 0 m. Displacement 0 Average velocity = = = 0 m s -1 ( 25 + 30) Time taken © Manhattan Press (H.K.) Ltd.

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4.2 Speed and velocity (SB p. 12)

Class Practice 3: A man is running on a road. His position at different instants are shown in the figure below. Complete the table, and take the direction to the right as positive.

Ans wer Time interval / s Displacement / m Average velocity / m s−1 © Manhattan Press (H.K.) Ltd.

0−5

5 − 10

15 15 5 =3

20 20 5 =4

10 − 20

20 − 30

30 −40 30 −40 = −4 =3 10 10

30 − 40

−30 −30 =3 10 10

4.2 Speed and velocity (SB p. 13)

Class Practice 4: An ant takes 10 minutes to walk from A to B along the path as shown in the figure. (a) What are the distance travelled and the average speed of the ant? Distance travelled 22 cm = _________________ Ans Average speed wer 0.22 = 3.7 × 10−4 m s−1 10 × 60 = _________________ © Manhattan Press (H.K.) Ltd.

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4.2 Speed and velocity (SB p. 13)

Class Practice 4 (Cont): (b) What are the displacement and average velocity of the ant? Displacement 2 cm (due north) = _________________ Ans Average velocity wer 0.02 = 3.3 × 10−5 m s −1 10 × 60 (due north) = _________________

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4.2 Speed and velocity (SB p. 13)

Instantaneous speed and instantaneous velocity To determine the average speed of a body: • distance travelled • time taken speed

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time → very short

Instantaneous speed

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4.2 Speed and velocity (SB p. 13)

Instantaneous speed and instantaneous velocity e.g. speedometer of a car measures its instantaneous speed

Similarly, Instantaneous velocity © Manhattan Press (H.K.) Ltd.

Velocity at a certain time 14

To section 4.3

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4.2 Speed and velocity (SB p. 8)

Activity 2 Speeds and distance

1. Can you estimate the speeds of the following objects? Fill in the blank with approximate Ans speeds. wer

3.0× 108m s−1

1.4 m s−1 9ms

−1

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100 m s−1 600 m s−1

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4.2 Speed and velocity (SB p. 8)

Activity 2 (Cont) Speeds and distance

2.

Have you ever heard of the Relativity theory proposed by Albert Einstein? Many strange things may happen when an object is travelling at the speed close to the speed of light. Try to find the related information and see whether you understand the theories. Return to

E = mc2 © Manhattan Press (H.K.) Ltd.

Text

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4.2 Speed and velocity (SB p. 10)

Thinking 3

In a highway, the speed limit for vehicles is 100 km h−1. Two electronic devices are set up along the road with a separation of 30 m. The time taken for a car to move through the two electronic devices is 0.8 s. Should a speeding ticket be issued to the driver of the car? Explain briefly. Ans wer © Manhattan Press (H.K.) Ltd.

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4.2 Speed and velocity (SB p. 10)

Thinking 3 (Cont):

Average speed of the car Distance travelled = Time taken 30 = 1 000 0.8 3 600 = 135 km h−1

The average speed exceeds the speed limit of 100 km h−1. Hence, a speeding ticket should be issued to the driver. Return to

Text © Manhattan Press (H.K.) Ltd.

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