Speed, velocity and acceleration

1 Both Mr Rabbit and Mr Tortoise took the same round trip, but Mr Rabbit slept & returned later.

Comment on their their argument.

Me, as I spent less time on the

trip.

No, I travelled longer distance every

minute.

Who runs faster?

radius = 8 km

O

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

scale = 1 cm : 5 km

(a) If he walks at a speed of 4 km h–1,try to locate his possible positions on the map.

radius = 8 km

O

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

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

The direction in which he has been walking.

scale = 1 cm : 5 km

1 SpeedHow 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 h–1.

1 Speed

Speed is a measure of how fast something moves.

Speed = distance travelled per unit of time

Speed = distance travelled per unit of timeSI unit: m s–1 or km h–1 (for long distances)

How can we describe how fast an object moves?

and speeds up again to 60 km h–1.and speeds up again to 60 km h–1.

a Average speed

Its average speed over the whole journeyoverall distance travelled

total time of travel

slows down to 0 km h–1, slows down to 0 km h–1,

A car travels at 50 km h–1,A car travels at 50 km h–1,

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.

a Average speed1 Speed

b Instantaneous speed

= speed at any instantInstantaneous speed

1 Speed

The word ‘speed’ alone instantaneous speedInstantaneous speed

distance travelled in an extremely short time interval

Simulation

Speedometer tells the car’s speed at any instant!

1 Speed

b Instantaneous speed

2 Velocity

rate of change of displacement.

a speed in a given direction or

velocitya

vector quantit

y

direction

magnitude(speed)

Velocity is...

speed = 300 km h–1

direction = west

MTR drivers concern speed only.

a Speed with direction

2 Velocity

Pilots concern velocity (direction & speed).

speed = 90 km h–1

b Average velocity

Average velocity =overall displacement

total time of travel

direction of velocity = direction of overall displacement

2 Velocity

c 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.

2 Velocity

Q1 The world record...

( )Average speed = 10.49

= 9.53 m s–1 or 34.3 km h–1

100

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

What is the average speed?

In an orienteering event, Maria and Karen reach their control points at the same time.

Q2 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 in a higher average velocity?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.

Who runs in a higher average velocity?Who runs in a higher average velocity?

Q2 In an orienteering event...

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.

Q3 True or false:

(T/F)

Average speed of an object magnitude of its average velocity.

A man takes a walk starting from rest and ending at rest.

Q4 True or false:

(T/F)

It is possible for him to attain an average speed of 5 km h–1 but he never goes faster than 5 km h–1.

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).

When a car changes direction,

its velocity changes too.

3 Acceleration

3 AccelerationAcceleration 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

=

If a car accelerates at 2 m s–2, what does that mean?

3 Acceleration

t = 1 sv = 2 m s–1,v = 2 m s–

1

v = 0

t = 2 sv = 4 m s–1, v = 2 m s–

1

v = 6 m s–1, v = 2 m s–1

t = 3 s

1 m

t = 0

3 m

5 m

Airport Express takes 0.35 h to go from HK station to Airport station (34 km).

Example 1

HK Kln

Kln Tsing Yi

Tsing Yi Airport

Distance between stations / kmJourney time between stations / sAve. speed between stations / km h–1

2.6

8.9

(a)

153

(b)

762

(c)

90

105

Ave. speed =34 km/0.35 h

Complete table.

= 97 km h–1

Example 1

HK Kln

Kln Tsing Yi

Tsing Yi Airport

Distance between stations / kmJourney time between stations / sAve. speed between stations / km h–1

2.6

8.9

(a)

153

(b)

762

(c)

90

105

(b) Kln Tsing Yi:

Time = distance / ave. speed= 8.9 / 90= 0.0989 h= 356 s

Example 1

HK Kln

Kln Tsing Yi

Tsing Yi Airport

Distance between stations / kmJourney time between stations / sAve. speed between stations / km h–1

2.6

8.9

(a)

153

(b)

762

(c)

90

105

(a) Tsing Yi Airport:

Distance = ave. speed time= 105 12.7

762 s = (762/3600) h= 12.7 h

= 22.2 km

Example 1

HK Kln

Kln Tsing Yi

Tsing Yi Airport

Distance between stations / kmJourney time between stations / sAve. speed between stations / km h–1

2.6

8.9

(a)

153

(b)

762

(c)

90

105

(c) HK Kln:

Ave. speed = distance / time= 2.6 / 0.0425

153 s = (153/3600) h= 0.0425 h

= 61.2 km

A man walks from A to B at 1 km h–1,

A B1 km h–1

Example 2

2 km h–1

and returns at 2 km h–1.

Average speed for the whole trip = ?

= 1.33 km h–1

A B1 km h–1

2 km h–1

Example 2

Suppose AB = 1 kmTime for whole trip = 11 h km 2

km 1h km 1

km 1

= 1 h + 0.5 h = 1.5 h

whole journey = 2 km

Ave. speed = distance / time= 2/1.5

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

C B

A

3 km

7 km

Example 3

(a) average speed,

Ave.

speed = distance travelledtime taken

= (7 + 3) km(10/60) h

= 60 km h–1

Example 3A car travels 7 km north and then 3 km west in 10 minutes. Find

C B

A

3 km

7 km

(b) ave. velocity?

AC = 22 BCAB 22 37 = 7.62 km

tan = =23.2o3/7

Example 3A car travels 7 km north and then 3 km west in 10 minutes. Find

C B

A

3 km

7 km

AC = 7.62 km, =23.2o

Size of ave.

velocity =

= 45.7 km h–1

displacementtime

7.62 km(10/60) h

=

Ave. velocity is 45.7 km h–1, 23.2° north of west.

(b) ave. velocity?

The Ferrari 348 can go from rest to 100 km h–1 in 5.6 s.

Example 4

What is its ave. acceleration (in m s–2)?Ave. acceleration

=100 km h–1

5.6 s(100/3.6) m s–1

5.6 s=

= 4.96 m s–2

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

Quantity Unit Scalar/Vector

Speed ______ _____

Velocity ______ _____

Change in velocity ______ _____

Acceleration ______ _____

Q2 When time is measured...

Unit of time: hour (h)

km h–1

km h–1

km h–1

km h–2

scalarvectorvectorvector

Unit of distance/displacement: kilometer (km)

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

In 2.5 s, a car speeds up from 60 km h–1 to 65 km h–1...

…while a bicycle goes from rest to 5 km h–1.

Which one has the greater acceleration?

They have the same 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?

What happens if it moves under a ve deceleration?

The car will slow down.

The car will move in +ve direction with increasing speed.