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Speed, velocity and acceleration

1 Both Mr Rabbit and Mr Tortoise took the same

round trip, but Mr Rabbit slept returned later.

Who runs faster?

No, I travelled longer distance every minute.

Me, as I spent less time on the trip.

Comment on their their argument.

2 A boy has been missing in a forest for 2 hours.

scale 1 cm 5 km

O

(a) If he walks at a speed of 4 km h1,

try to locate his possible positions on the map.

2 A boy has been missing in a forest for 2 hours.

scale 1 cm 5 km

O

(b) What else is important to spot the boy?

The direction in which he has been walking.

1 Speed

- How can we describe how fast an object moves?

E.g. A car on Tolo Highway travels 90 km in 1

hour.

We say that the car travels at a speed of 90 km

h1.

1 Speed

How can we describe how fast an object moves?

Speed is a measure of how fast something moves.

Speed distance travelled per unit of time

SI unit m s1

or km h1 (for long distances)

a Average speed

1 Speed

A car travels at 50 km h1,

slows down to 0 km h1,

and speeds up again to 60 km h1.

Its average speed over the whole journey

overall distance travelled

total time of travel

a Average speed

1 Speed

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.

b Instantaneous speed

1 Speed

Instantaneous speed

- speed at any instant

The word speed alone ? instantaneous speed

Instantaneous speed ? distance travelled in an

extremely short time interval

Simulation

b Instantaneous speed

1 Speed

Speedometer tells the cars speed at any instant!

2 Velocity

Velocity is...

a speed in a given direction or

rate of change of displacement.

a vector quantity

velocity

a Speed with direction

2 Velocity

MTR drivers concern speed only.

speed 90 km h1

Pilots concern velocity (direction speed).

speed 300 km h1 direction west

b Average velocity

2 Velocity

overall displacement

Average velocity

total time of travel

direction of overall displacement

direction of velocity

c Instantaneous velocity

2 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.

Q1 The world record...

The world record of women 100-m race is 10.49 s.

What is the average speed?

100

9.53 m s1 or 34.3 km h1

Q2 In an orienteering event...

In an orienteering event, Maria and Karen reach

their control points at the same time.

start, 1000 am

Maria, 1030 am

Karen, 1030 am

Who runs in a higher average velocity?

Q2 In an orienteering event...

Who runs in a higher average velocity?

A Maria. B Karen. C Undetermined since their

paths are unknown. D Incomparable since they run

along different directions.

Q3 True or false

Average speed of an object ? magnitude of its

average velocity.

(T/F)

Note The distance travelled is equal to

magnitude of displacement only if it is a

straight-line motion. Speed is usually larger

than the magnitude of velocity.

Q4 True or false

A man takes a walk starting from rest and ending

at rest.

It is possible for him to attain an average speed

of 5 km h1 but he never goes faster than 5 km

h1.

(T/F)

3 Acceleration

- When a car moves faster and faster,

its speed is increasing (velocity changed).

3 Acceleration

When a car moves slower and slower,

its speed is decreasing (velocity changed).

3 Acceleration

When a car changes direction,

its velocity changes too.

3 Acceleration

Acceleration measures the change in velocity

Acceleration ?velocity per unit time

overall change in velocity

total time taken

vector quantity

m s2

Unit m s1 / s

3 Acceleration

If a car accelerates at 2 m s2, what does that

mean?

v 0

t 0

v 2 m s1, ?v 2 m s1

t 1 s

1 m

v 4 m s1, ?v 2 m s1

t 2 s

3 m

t 3 s

v 6 m s1, ?v 2 m s1

5 m

Example 1

Airport Express takes 0.35 h to go from HK

station to Airport station (34 km).

? Ave. speed

34 km/0.35 h

97 km h1

Complete table.

Example 1

(b) Kln ? Tsing Yi

distance / ave. speed

Time

8.9 / 90

0.0989 h

356 s

Example 1

(a) Tsing Yi ? Airport

Distance

ave. speed ? time

105 ? 12.7

22.2 km

762 s (762/3600) h 12.7 h

Example 1

(c) HK ? Kln

distance / time

Ave. speed

2.6 / 0.0425

61.2 km

153 s (153/3600) h 0.0425 h

Example 2

A man walks from A to B at 1 km h1,

and returns at 2 km h1.

1 km h1

A

B

Average speed for the whole trip ?

Example 2

1 km h1

A

B

? whole journey 2 km

Suppose AB 1 km

Time for whole trip

1 h 0.5 h 1.5 h

Ave. speed distance / time

2/1.5

1.33 km h1

Example 3

A car travels 7 km north and then 3 km west in 10

minutes. Find

(a) average speed,

Ave. speed

3 km

B

C

distance travelled

time taken

7 km

60 km h1

A

Example 3

A car travels 7 km north and then 3 km west in 10

minutes. Find

(b) ave. velocity?

3 km

B

C

AC

7 km

7.62 km

tan q

? q 23.2o

3/7

A

Example 3

A car travels 7 km north and then 3 km west in 10

minutes. Find

(b) ave. velocity?

3 km

AC 7.62 km, q 23.2o

B

C

Size of ave. velocity

displacement

7.62 km

7 km

time

(10/60) h

45.7 km h1

Ave. velocity is 45.7 km h1, 23.2 north of west.

A

Example 4

The Ferrari 348 can go from rest to 100 km h1

in 5.6 s.

What is its ave. acceleration (in m s2)?

Ave. acceleration

4.96 m s2

Q1 A running student...

A running student is slowing down in front of a

teacher.

With reference to the sign convention,

Velocity of student positive / negative

Acceleration of student positive / negative

Q2 When time is measured...

Unit of time hour (h)

Unit of distance/displacement kilometer (km)

Quantity Unit

Scalar/Vector Speed ______

_____ Velocity ______

_____ Change in velocity ______

_____ Acceleration ______

_____

km h1

scalar

km h1

vector

km h1

vector

km h2

vector

Q3 In 2.5 s, a car speeds up...

In 2.5 s, a car speeds up from 60 km h1 to 65 km

h1...

while a bicycle goes from rest to 5 km h1.

Which one has the greater acceleration?

They have the same acceleration!

Q4 A car is moving in positive...

A car is moving in ve direction.

What happens if it moves under a ?ve

acceleration?

The car will slow down.

What happens if it moves under a ?ve

deceleration?

The car will move in ve direction with

increasing speed.

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