## 138063711 Kiss Notes Moving About Essay

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Preliminary Physics Topic 3

What is this topic about?
To keep it as simple as possible, (K.I.S.S.) this topic involves the study of: 1. SPEED and VELOCITY
2. FORCE and ACCELERATION
3. WORK and KINETIC ENERGY
4. MOMENTUM and IMPULSE
5. SAFETY DEVICES in VEHICLES

...all in the context of moving vehicles.

but first, let’s revise...
WHAT IS SPEED?

WHAT IS ENERGY?

“Speed” refers to how fast you are going.
You already know that mathematically:

Energy is what causes changes....
change in temperature (Heat energy)
change in speed (Kinetic energy)
change in height
(gravitational Potential energy)
change in chemical structure
(chemical P.E.)
...and so on.

SPEED = distance travelled
time taken
In this topic, you will extend your understanding
of speed to include VELOCITY, which is just a
special case of speed.

In this topic the most important energy form you
will study is the one associated with moving
vehicles...

WHAT IS FORCE?
A FORCE is a PUSH or a PULL.

KINETIC ENERGY

Some forces, like gravity and electric/magnetic
fields, can exert forces without actually
touching things. In this topic you will deal
mainly with CONTACT FORCES, which push or
pull objects by direct contact.

WHAT MAKES A CAR GO?
Overview
of Topic:

ENGINE provides ENERGY
(from chemical energy
in petrol)

Tyres PUSH on road...
FORCE acts...

FORCE causes

ACCELERATION
In the context of moving vehicles, the most
important force is FRICTION. Friction allows a
car’s tyres to grip the road to get moving, and
for the brakes to stop it again. Without friction
the car couldn’t get going, and couldn’t stop if it
did!
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FORCE acts over
a distance...
“WORK” done

KINETIC
ENERGY
changes

VELOCITY
changes
1

MOMENTUM
changes

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CONCEPT DIAGRAM (“Mind Map”) OF TOPIC
Some students find that memorising the OUTLINE of a topic helps them learn and remember the concepts and important facts. As you proceed through the topic, come back to this page regularly to see how each bit fits the whole. At the end of the notes you will find a blank version of this “Mind Map” to practise on.

Average &
Instantaneous
Speed

Motion
Graphs
Forces
Vectors & Scalars.
Speed & Velocity

Vectors

Acceleration

Mass
&
Weight

Measuring
Motion

Speed
&
Velocity

Force
&
Acceleration

Newton’s
2nd Law

Centripetal
Force

MOVING

Work
&
Kinetic Energy
Energy
Transformations

Safety Devices
in
Vehicles

Momentum
&
Impulse

Equivalence of
Work & Energy
Law of
Conservation
of Energy
Momentum

Physics of
Safety
Devices

Inertia
&
Newton’s
1st Law

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Newton’s
3rd Law

Impulse
of a Force

Conservation
of Momentum
in Collisions
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1. SPEED & VELOCITY
Average Speed for a Journey
If you travelled by car a distance of 300 km in exactly 4 hours, then your “average speed” was: average speed

=

distance travelled
time taken

=

300
4

=

75 km/hr (km.hr-1)

However, this does not mean that you actually travelled at a speed of 75 km/hr the whole way. You probably went faster at times, slower at other times,
and may have stopped for a rest at some point.

Distance-Time Graphs

Speed-Time Graphs

Perhaps your journey was similar to this graph.

The same journey could also be represented by
a different graph, showing the SPEED at
different times:

Start at the bottom-left of the graph and consider
each section A, B, C and D.

100

These graphs
represent the
same journey

A

0

1

2
3
TIME (hours)

4

1

Stopped.
Speed scale
2
TIME (hr)

3

4

This graph is very unrealistic in one way. It
shows the speed changing INSTANTLY from
(say) 100 km/hr to zero (stopped), without any
time to slow down. It also shows the car
travelling at exactly 100 km/hr for an hour at a
time... very unlikely with hills, curves, traffic etc.

This raises the idea of INSTANTANEOUS
SPEED: the speed at a particular instant of time.
The speedometer in your car gives you a
speed... this is your instantaneous speed.

Changes of speed (ACCELERATION) will be
dealt with in the next section. For now we’re
Keeping It Simple!

On the graph, the GRADIENT at any given point
is equal to INSTANTANEOUS SPEED.

SPEED-TIME GRAPHS
show the SPEED of a moving object
at each TIME.

DISTANCE-TIME GRAPHS
show the DISTANCE (from the starting point)
at each TIME.
The GRADIENT at any point equals
INSTANTANEOUS SPEED.

The speed at any time can be read from
the vertical scale of the graph.
A horizontal section means that
the object was moving at constant speed.

A horizontal section means that
the object was not moving
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B
0

So although the average speed for the entire
journey was 75km/hr, in fact you never actually
moved at that speed.

“Flat” parts
DO NOT
mean
stopped,
but mean
constant
speed

C

20

i.e. stopped

SPEED (km/hr)
40
60
80

300

C
B

D

A

0

Graph section A
Travelled 100 km
in 1.0 hour:
Speed =100 km/hr

You must not confuse the 2 types of graph and
how to interpret them.
D

50

Graph section B
Zero distance
moved in 0.5 hr:
Speed= zero.

time
= speed

0

Graph section C
Travelled 50 km
in 1.0 hr:
Speed=50 km/hr

Study this graph carefully and compared it with
the other...

Distance-T
Time Graph

DISTANCE TRAVELLED (km)
100
150
200
250

Graph section D
Travelled 150km
in 1.5 hr:
Speed = 100 km/hr

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Scalars & Vectors
A Scalar quantity is something that has a size
(magnitude) but no particular direction.
A Vector quantity has both size (magnitude) AND
DIRECTION.

BUT, consider the “NET journey”: at the end of
the journey you end up 30 km EAST of the
starting point. So, your final displacement is “30
km east”.

So far we have dealt with only distances &
speeds... these are Scalar quantities, since they
do not have any special direction associated.

The VECTOR journey was:
• travelled 30 km east displacement in 1.5 hours.
• average velocity = 30/1.5 = 20 km/hr east.

Now you must learn the vector equivalents:
“Displacement” = distance in a given direction,
and
“Velocity” = speed in a given direction.

Notice that both displacement and velocity have
a direction (“east”) specified....
they are
VECTORS!
To make better sense (mathematically) of the
journey, the directions east & west could have
(+) or ( - ) signs attached. Let east be (+) and
west be ( - ).
Then the total
Average = Displacement
journey
Velocity
time
displacement was

Consider this journey:
drove 60 km EAST in 1 hour
START
then
drove 30 km WEST
in 0.5 hour.

(+60) + (-30) = +30 km.

Vav = S
t

As a SCALAR journey:
• travelled a total 90 km distance in 1.5 hours,
• average speed = 90/1.5 = 60 km/hr

Note: The symbol “S” is used for Displacement

MORE GRAPHS... Displacement - Time

...and the corresponding Velocity - Time Graph:
100

Refer to the previous Distance-Time graph.
What if the 300km journey had been 150 km north
(sections A, B, C) then 150 km south (section D)?

Back at starting point.
(Displacement = 0 )
1

2
TIME (hours)

3

4

In vector terms; displacement north is positive (+)
displacement south is negative ( - )

In section D:
displacement = -150 km (south)

C

TIME (hrs)

B
1
Zero velocity:
means stopped

2

3

4

Negative value:
south-b
bound
velocity
D

The velocity values for each part of this graph
are equal to the gradients of the corresponding
parts of the Displacement - Time Graph.
Note: Since the journey ends back
at the starting point,
total displacement = zero
and average velocity = zero
for the whole trip.

velocity = displacement
time
= -150 /1.5
= -100 km/hr (i.e. 100km/hr southward)
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0
-1
100

0

south
-5
50

po
sit
ive
Gr
ien
t

D

ve
ati
neg

Displacement NORTH (km)
0
50
100

nt
die
Gra

B

Velocity (km/hr)

150

Downsloping
line means
travelling
SOUTH

C

A

north
50

The Displacement - Time Graph would be:

Positive values mean
north-b
bound velocity

A

However, this simply points out how little
information the “average” gives you.
The instant-by-instant Physics of the
journey is in the graph details.
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Measuring Motion

Prac Work:
You will probably experience one or more of these commonly used ways to measure motion in the laboratory.

You might do some measurements as
suggested by this diagram
Time to travel from A to B measured by stopwatch

Distance between landmarks measured with sports tape

Landmark
A

Tape Measure & Stopwatch
The simplest method of all: measure the distance
or displacement involved, and the time taken.
Then use
speed (velocity) = distance (displacement)
time
Typical Results
Distance
Time
Velocity
(m)
(s)
(ms-1)
Car
Bicycle

87
87

6.2
22.4

Landmark B

The “Ticker-Timer”
Every time the hammer hits the
moving strip of paper
it leaves a dot.
The string of dots can be
analysed to study the
motion of the trolley.

Moving lab. trolley
drags a strip of
paper behind it

“Ticker-ttimer” device has a small hammer
which vibrates up and down every 0.02 sec.

14.0
3.9

However, this can only give you the AVERAGE
speed or velocity. In Physics we often need to
consider INSTANTANEOUS velocity.

Although this method is very out-dated, it is
still commonly used as a way for
students to learn how to measure
instantaneous velocity.
A moving object drags a paper strip on
which dots get printed (usually every 0.02
second) as it goes. The gap between dots is
a record of displacement and time. This
allows you to calculate the velocity over
every 0.02 s. It’s still an average, but over
such small time intervals it approximates
the instantaneous velocity.

Electronic or Computer Timing
You may use devices that use either “Light
Gates” or “SONAR” to record displacements
and times for you.
Once again, any velocities calculated are
averages, but the time intervals are so short
(e.g. as small as 0.001 s) that the velocity
calculated is essentially instantaneous.
Moving trolley equipped with a
sonar reflector.
(An aluminium pie dish will do)

Sonar “transponder” gives out
pulses of ultra-s
sound and picks
up any returning echoes

To computer for
analysis

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Worksheet 1

Speed & Velocity

Fill in the blank spaces.

Student Name...........................................
On a displacement-time graph, movement south
would
result
in
the
graph
sloping
m)................................... to the right and having a negative n)............................................

The average speed of a moving object is equal
to the a)............................ travelled, divided by
b)....................... taken. On a Distance-Time
graph, the c)........................ of the graph is equal
to speed. A horizontal graph means
d)................................. ...............................

The
vector
equivalent
of
speed
is
o).................................... The average velocity is equal to p)............................... divided by
q)....................... Instantaneous velocity refers to
r)..................................................................

On a Speed-Time graph, constant speed is
shown by e).......................................... on the graph. This does NOT mean stopped, unless the
graph section is lined up with f).............................

Laboratory methods for measuring motion
include using a tape measure and stopwatch.
This allows calculation of s)....................
............................ only. “Ticker-timers” record both t)............................... and .......................... on a paper tape. Average velocity can be calculated
for short time intervals which are approximately
equal to u)............................................ velocity. • Electronic or Computer-based devices often
use v)........................ or ......................................... to gather displacement, time and velocity data at
very short time intervals.

Speed and distance are both g).............................. quantities, because the direction doesn’t matter.
Often in Physics we deal with h)............................ quantities, which have both i)............................... and .......................................
The vector equivalent of distance is called
j)................................., and refers to distance in a particular k).............................. For example, if
displacement was being measured in the north
direction, then a distance southward would be
considered as l).............................. displacement.

Worksheet 2
Motion Graphs

Practice Problems
Student Name...........................................

A car travelled 200 km north in 3.0 hours, then
stopped for 1.0 hr, and finally travelled south 100
km in 1.0 hr.
1. What was the total distance travelled?

7. Use your graph to find:
i) average velocity for the first 3 hours.

ii) velocity during the 4th hour.
2. What was the total displacement?
iii) velocity during the last hour.
3. What was the total time for the whole journey?
4. Calculate the average
speed for the whole journey.

North

100

8. Construct a Velocity- Time Graph for this trip.

Time (hr)

0

Velocity (km/hr)

1

2

3

4

5

-1
100

South

-5
50

Displacement

6. Construct a
Displacement - Time
Graph for this trip.

50

5. Calculate the average velocity for the whole
journey.

TIME
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Worksheet 3
Practice Problems
Motion Graphs & Calculations
800

1. An aircraft took
off from town P and
flew due north to
town Q where it
stopped to re-fuel. It
then flew due south
to town R.

UNITS OF MEASUREMENT
So far all examples have used the familiar
km/hr for speed or velocity. The correct S.I.
units are metres per second (ms-1). You need
to be able to work in both, and convert from
one to the other.....
here’s how:
1 km/hr = 1,000 metres/hr
= 1,000m/(60x60) seconds
= 1,000/3,600 m/s
= 1/3.6
So, to convert km/hr
ms-1 divide by 3.6
to convert ms-1
km/hr multiply by 3.6

200

400

600

Displacement north (km)

Q

P

Time
(hr)
1

2

3

4

5

-4
400 -2
200

The trip is
summarised by the
graph.

Student Name...........................................

6

R

a) How far is it from towns P to Q?

2. A car is travelling at 100 km/hr.
a) What is this in ms-1?

b) How long did the flight P to Q take?
c) Calculate the average velocity for the flight
from P to Q (include direction)

b) The driver has a “micro-sleep” for 5.00 s. How far
will the car travel in this time?
c) At this velocity, how long does it take (in seconds)
to travel 1.00km (1,000m)?

d) What is the value of the gradient of the
graph from t=3 hr, to t=6 hr.?

3.
For this question consider north as (+), south as ( - ).

e) What part of the journey does this
represent?

A truck is travelling at a velocity of +20.5 ms-1 as it
passes a car travelling at -24.5 ms-1.

f) Where is town R located compared to town P?
a) What are these velocities in km/hr? (including
directions?)

g) What was the aircraft’s position and velocity
(including direction) at t=5 hr?

b) What is the displacement (in m) of each vehicle in
30.0 s?

h) What was the:
i) total distance
c) How long would it take each vehicle to travel
100 m?

ii) average speed
iii) total displacement

4. Where does this aircraft end up in relation to its
starting point?

iv) average velocity
(for the entire 6 hr journey)

Next, flew east at 105 ms-1 for 50.0 minutes.

100

200

Velocity (km/hr)
North

Next, flew west for 3.25 hours at 325 km/hr.
Time (hr)

0

i) Construct a
Velocity- Time
Graph for
the flight.

300

400

Flight details:
First flew west for 2.50 hr at 460 km/hr.

2

3

4

5

6

Finally flew east for 5.50 hours at velocity 125 ms-1.

-3
300

South

-1
100

1

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2. FORCE & ACCELERATION
Graphs of Accelerating Vehicles

Change of Velocity = Acceleration

You may have done laboratory work to study the
motion of an accelerating trolley. If you used a
“Ticker-timer”, the paper tape records would
look something like this:

Any change in velocity is an acceleration.
Mathematically,
acceleration = velocity change = final vel. - initial velocity time taken
time taken

Tape of trolley accelerating... dots get further apart

v = final velocity
u = initial velocity
t = time involved

Trolley decelerating (negative acceleration)... dots get closer

Units: if velocities are in ms-1, and time in
seconds, then acceleration is measured in
metres/sec/sec (ms-2).

The graphs that result from acceleration are as
follows:

Explanation: Imagine a car that accelerates at 1 ms-2:
1 sec. later
v = 1 ms-1

1 sec.later
v=2 ms-1

Remember,
equals
Velocity

1sec.later
v=3ms-1

Displacement

Every second, its velocity increases by 1 ms-1.
Therefore, the rate at which velocity is changing
is 1 ms-1 per second, or simply 1 ms-2.
Acceleration is a vector, so direction counts.

+
ACCELERATION
VECTOR

VELOCITY
VECTOR

DISPLACEMENT-T
TIME GRAPH
(curve flattens out)

THIS CAR IS SLOWING
DOWN... DECELERATING

ing
rat
ele
c
De

(straight line)

(curve gets steeper)

Time

“Deceleration” (or negative acceleration) simply
means that the direction of acceleration is
opposite to the current motion... the vehicle will
slow down rather than speed up.

VELOCITY-T
TIME GRAPH
Constant
Velocity

A motorcycle travelling at 10.0 ms-1, accelerated
for 5.00s to a final velocity of 30.0 ms-1. What was
its acceleration rate?

Velocity
increasing

Solution: a = v - u = 30.0-10.0/5.00 = 20.0/5.00
t
= 4.00 ms-2.

A common error is to
think that this means the
object is moving
backwards. Wrong! It is
moving forward, but
slowing down.

g
in
at
ler
ce
De

Velocity

Example Problem 1

Ac
ce
ler
at
in
g

Start
v =0

Co
Ve nsta
loc nt
ity

a=v-u
t

Δ (Greek letter “delta”) refers
to a change in a quantity

Ac
ce
le
ra
tin
g

a = Δv
Δt

Tape of trolley moving at constant velocity (for comparison)

Velocity
decreasing

Velocity = 0
∴ Stopped!

Example Problem 2

A car moving at 25.0 ms-1 applied its brakes
producing an acceleration of -1.50 ms-2
(i.e. deceleration) lasting for 12.0 s.
What was its final velocity?
Solution: a = v - u,
t

Time

so v = u + at
= 25.0 + (-1.50) x 12.0
= 25.0 - 18.0
= 7.00 ms-1.

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On a Velocity-T
Time Graph

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Force Causes Acceleration

PRESSING ON THE ACCELERATOR...

A simple definition of “Force” is a push or a pull.
However, in the context of moving vehicles,

Weight

Vertical forces are
balanced, and cancel

Force is what causes
velocity to change.

Thrust Force
Increased

Note that a change of velocity could mean:
• speeding up
• slowing down
• changing direction (velocity is a vector)

Friction &
Air Resistance
small forces

Horizontal forces
UNBALANCED

Reaction
Force

To actually result in a change of velocity, the
force must be
External

and

For example, if you were
inside a moving car and
kicked the dashboard,
this force would have NO
EFFECT on the car’s
motion...
This is an “Internal Force”
and cannot cause
acceleration.

TURNING THE STEERING WHEEL...

Unbalanced (Net) Force

Vertical forces are
balanced, and cancel

Forward & Back
Forces are balanced
and cancel
WEIGHT FORCE
Car pushes on Earth

(Thrust Force from
Engine is equal to
Friction forces)
Sideways
Forces become
UNBALANCED
(These would
be equal if
wheel not
turned)

Thrust
from
Engine

Friction
and Air
Resistance

This car will
SPEED UP

REACTION FORCE
Earth pushes back

This car will turn a corner
at constant speed
(but this is a changed velocity
since the direction changed)

BALANCED & UNBALANCED FORCES
GOING UP A HILL
(without increasing engine thrust)

The car above has a number of forces acting on
it, but they are BALANCED... those acting in the
same line are equal and opposite,
and cancel each other out.
This car will not alter its velocity or direction; it
will not accelerate. It is either travelling at a
constant velocity, or it is stationary.
EXAMPLES OF
BALANCED
UNBALANCED
FORCE
FORCES
SITUATION

Engine Thrust
still the same

Part of the
Weight Force acts
downhill to cancel
some of the thrust

Reaction Force is not
vertical, and no
longer cancels the
weight completely...
UNBALANCED FORCE

This bike will SLOW DOWN.
(Going down a hill, it will speed up)

PASSING OVER AN ICY PATCH ON THE ROAD
Opposite Forces are
BALANCED and cancel

Friction
still the
same

Weight (still vertical)

Weight

PRESSING ON THE BRAKES...
Virtually no
Thrust Force
because tyres
can’t grip on ice
This car will continue
in a straight line, at a
constant velocity...
whether the driver
wants to or not...

Vertical forces are
balanced, and cancel

Virtually
no Friction
on Ice

Weight

Thrust Force
decreases as

Friction
Increases as
Brakes are
applied

accelerator is
released

Reaction Force
cancels Weight
Car is out of control;
Can’t stop...
Can’t turn...

Preliminary Physics Topic 3 “Moving About”