## Course curriculum

• 1

### 6.1 Mechanics

• Outline

• Motion in a straight line

• Example 1

• Example 1 Video

• Motion as a Function of Displacement or Velocity

• Velocity, Displacement and Time

• Example 2

• Example 2 Video

• The Solution

• A note on integration

• Acceleration and Velocity

• Proof 3

• Example 3 Video

• As a generalisation we will use:

• Example 4

• Example 4 Video

• Graphing

• Example 5

• Example 5 Video

• Example 5 Video (continued)

• Example 6

• Example 6 Video

• Horizontal Axes

• 2

### 6.2 Motion Without Resistance

• Further Motion in a Straight Line

• Hints for Success

• To successfully solve Mechanics questions:

• UNIT OF FORCE

• NEWTON’S LAWS

• NEWTON’S FIRST LAW

• NEWTON’S SECOND LAW

• Normal Force - an adjustable pushing force

• Tension - an adjustable pulling force

• Friction - An adjustable lateral Pushing force

• Example 1

• Example 1 Video

• Letting 𝜙=1

• Example 2

• Example 2 Video

• Letting 𝑔=10

• Gravity

• Example 3

• Example 3 video

• Vertical Scale

• 3

### 6.3 Simple Harmonic Motion

• SHN

• Rubber Band Example

• Speed

• Terminology and Definitions

• EquationS of Motion

• Proof 1

• Proof 1 Example

• The PURPOSE of 𝑛 and 𝛼 on the Equation of Motion

• Simple Harmonic Motion

• Example 2

• Example 2 Video

• Example 3

• Example 3 Video

• Example 4

• Example 4 Video

• Example 5

• Example 5 Video

• Example 6

• Graphs of Sim

• Example 6 Video

• Example 7

• Example 7 Video

• 4

### 6.4 Harder Simple Harmonic Motion

• Alternative Equations of Motion

• Example 1

• Example 1 Video

• Velocity as a function of displacement

• Proof 2

• Example 2 Video

• Example 2 Video (continued)

• Example 3

• Example 3 Video

• Example 4

• Example 4 Video

• Example 5

• Example 5 Video

• Example 6

• Example 6 Video

• 5

### 6.5 Horizontal Resisted Motion

• In real life situations ...

• Resisted Motion

• RESISTANCE AND HOW IT IS MODELLED

• Gravity

• Example 1

• Example 1 Video

• Letting K = 1

• Example 2

• Example 2 Video

• The particle increases ...

• Example 3

• 6.53

• Letting 𝑢=10

• 6

### 6.6 Vertical Resisted Motion

• Vertical Resisted Motion

• Rising Objects

• Falling Objects

• Constant gravitational acceleration

• TERMINAL VELOCITY

• UNDERSTANDING TERMINAL VELOCITY

• Example 1

• Example 1 Video

• Celocity approaches

• Example 2

• Example 2 Video

• Note that the values of 𝑘

• Example 3

• Example 3 Video

• Example 3 Video (continued)

• Graphing

• 7

### 6.7 Further Projectile Motion - Cartesian Equations

• Cartesian equation

• Example 1 (Extension 1 level)

• Example 1 Video

• Cartesian Equations in Extension 2

• Proof 2

• Example 2 Video

• Example 3

• Example 3 Video

• Example 4

• Example 4 Video

• Harder Projectile Motion

• Example 5 (2019 HSC)

• Example 5 Video

• Example 5 Video (continued)

• 8

### 6.8 Projectile Motion with Resistance

• Projectile Motion with Resistance

• Particles that rise then fall

• Example 1 (2013 HSC)

• Example 1 Video

• Example 1 Video (continued)

• Example Video 1 (continued)

• Example 2

• Example 2 Video

• Example 2 Video (continued)

• Example 2 Video (continued)

• RESISTED PROJECTILE MOTION AT AN ANGLE TO THE HORIZONTAL

• The blue line ...

• In summary

• Example 3

• Example 3 Video

• SPLITTING AIR RESISTANCE INTO COMPONENTS

• Linear Drag

• Proof 5

• Example 5 Video

• Quadratic Drag

• Proof 6

• Example 6 Video

• VERTICAL AND HORIZONTAL ACCELERATION

• Example 3

• Example 3 Video

• Example 4 (2003 HSC)

• Example 4 Video

• Example 4 Video (continued)

• Example 4 (continued)

• Example 4 (continued)

• In this past HSC question ...

## Instructor Steven Howard

Steve is a Mathematics Teacher at Cowra High School, a medium sized rural high school in Central West NSW, where he has taught for over 25 years. He has also taught gifted and talented students online through xsel and Aurora College. He has a particular love and passion for Mathematics Extension 2, writing his own textbook and study resources for the new syllabus, which you can access from any of his courses. He loves finding more efficient techniques for solving mathematical questions, by trawling through other teachers' solutions or making up his own approaches when there must be a better way. Steve did 4 Unit Mathematics as a student, gaining a mark of 198/200 and training as an actuary. Working in an office in the city wasn't for him, so he went back to uni to retrain as a maths teacher then headed to the country, where he lives in an owner built mud house, with chickens, goats and rescued native birds (which you will sometimes hear in his recordings)!!