Applications of Calculus to Mechanics

Functions of Displacement: Example Question.
Functions of Displacement: Harder Example (1 of 3 - Finding v²).
Functions of Displacement: Prologue.
Functions of Displacement: Proof 1.
Functions of Displacement: Proof 2.
Functions of Displacement: Harder Example (2 of 3 - Integrating for x).
Functions of Displacement: Harder Example (3 of 3 - Establishing Domain for v).
Gravity & Escape Velocity (1 of 3).
Gravity & Escape Velocity (2 of 3).
Gravity & Escape Velocity (3 of 3).
Introduction to Simple Harmonic Motion.
Simple Harmonic Motion: Basic Equations.
Characteristics of Simple Harmonic Motion (1 of 2).
Characteristics of Simple Harmonic Motion (2 of 2).
Simple Harmonic Motion: Amplitude Example.
Simple Harmonic Motion: Shifted Centre Example (1 of 2).
Simple Harmonic Motion: Shifting the Centre.
Simple Harmonic Motion: Shifted Centre Example (2 of 2).
Projectile Motion: North Korean Tank (1 of 4).
Projectile Motion: North Korean Tank (2 of 4).
Projectile Motion: North Korean Tank (3 of 4).
Projectile Motion: Summary of Equations.
Projectile Motion: Glenn Mcgrath (1 of 2).
Projectile Motion: Glenn Mcgrath (2 of 2).
Projectile Motion: North Korean Tank (4 of 4).
Projectile Motion: Colliding Particles (1 of 3).
Projectile Motion: Colliding Particles (2 of 3).
Projectile Motion: Colliding Particles (3 of 3).
Tricky Projectile Question: Different Angles of Projection.
Tricky Projectile Question: Equation of Path.
Tricky Projectile Question: Restriction on Angles.
Interpreting Displacement-Time Graphs.
Integrating Motion Equations: The Tennis Ball (1 of 3).
Integrating Motion Equations: The Tennis Ball (2 of 3).
Integrating Motion Equations: The Tennis Ball (3 of 3).
Introduction to Simple Harmonic Motion: Time Equations.
Key Illustration for Understanding Simple Harmonic Motion.
Physical Models and their Differential Equations.
Simple Harmonic Motion Example Question: The Spring.
Understanding SHM by examining its graphs.
Introductory Guide to Describing Motion.
Velocity as a Function of Displacement.
Acceleration in terms of Velocity (1 of 2: Review).
Acceleration in terms of Velocity (2 of 2: Derivation & Example).
The Ball & Stone (1 of 2: Finding Time of Collision).
The Ball & Stone (2 of 2: Determining Restriction on V).
Simple Harmonic Not-Motion: Fluctuating Temperature.
Projectile Motion: Simple Worked Example (1 of 4: Resolving Initial Velocity).
Projectile Motion: Simple Worked Example (2 of 4: Developing 4 Time Equations).
Projectile Motion: Simple Worked Example (3 of 4: Understanding the Point of Impact).
Projectile Motion: Simple Worked Example (4 of 4: Equation of Path).
Projectile Motion: Aiming for a Target (1 of 2: Generating Time Equations).
Projectile Motion: Aiming for a Target (2 of 2: Determining Firing Angle).
Relationship Between High & Low Firing Angles.
Equation of Path Example Question (1 of 2): Identifying Important Features.
Equation of Path Example Question (2 of 2): Adding in a Slanted Road.
Equation of Path: Understanding Time as the Parameter.
Mid-Air Target Question (1 of 4): Time of Equal Horizontal/Vertical Displacement.
Mid-Air Target Question (2 of 4): Time of Impact.
Mid-Air Target Question (3 of 4): Implied Restriction on Firing Angle.
Mid-Air Target Question (4 of 4): Two Final Results.
Exam Problem: Simple Harmonic Motion with Auxiliary Angle.
Defining Momentum & Force.
Introduction to Mechanics.
Newton's First Law: Inertia.
Mechanics Example 1: Using F = ma to find v(t).
Newton's Second Law: Inertial Mass.
Newton's Third Law: Reactions.
Mechanics Example 2: Using F = ma to find v(x).
Mechanics Example 3: Starting from Displacement Function.
Mechanics Example 4: Calculating Total Distance of a Multi-Step Journey.
Weight.
Introduction to Resisted Motion (1 of 2: What is Resistance?).
Introduction to Resisted Motion (2 of 2: Example question).
Resistance - should it be kv or mkv? (1 of 3: Introductory thoughts).
Resistance - should it be kv or mkv? (2 of 3: Inferring from details in the question).
Resistance - should it be kv or mkv? (3 of 3: What to do when it's ambiguous).
Vertical Resistance & Gravity example question (1 of 2: Finding x(v)).
Vertical Resistance & Gravity example question (2 of 2: Proving Final Result).
Vertical Resistance & Gravity: Framing the Question.
Mechanics Example 5: Momentum, Terminal Velocity & Total Distance.
Physics vs. "Motion" in Mathematics (1 of 2: What's included?).
Physics vs. "Motion" in Mathematics (2 of 2: What's different?).
Types of Motion in HSC Mathematics (2U, Ext 1 & Ext 2).
Introduction to Simple Harmonic Motion (1 of 2: Key Features).
Introduction to Simple Harmonic Motion (2 of 2: Time Equations).
Simple Harmonic Motion Question (1 of 3: Basic Features).
Simple Harmonic Motion Question (2 of 3: Extreme Values).
Harder SHM Question (1 of 5: Interpreting the question).
Harder SHM Question (2 of 5: Setting up the equations).
Harder SHM Question (3 of 5: Determining specific times).
Simple Harmonic Motion Question (3 of 3: Other Characteristics).
Harder SHM Question (4 of 5: Examining the geometry of movement).
Harder SHM Question (5 of 5: Determining specific speed).
Alternate Forms for Simple Harmonic Motion (Example 1 of 2).
Alternate Forms for Simple Harmonic Motion (Example 2 of 2).
Motion as Functions of Displacement (1 of 2: Why it matters).
Motion as Functions of Displacement (2 of 2: Example question).
Full Derivation of Acceleration = d(½v²)/dx.
Using d(½v²)/dx without SHM (1 of 2: Understanding Velocity).
Using d(½v²)/dx without SHM (2 of 2: Reintroducing Time).
Using the d(½v²)/dx result (1 of 2: The vertical spring).
Using the d(½v²)/dx result (2 of 2: Rest Position & Max Speed).
Differential Equations for SHM (1 of 2: A curious pattern).
Differential Equations for SHM (2 of 2: Deriving v²=n²[a²-x²]).
Projectile Motion (1 of 5: Defining Conditions for Projectile Motion and how time is built into it).
Projectile Motion (2 of 5: Outlining relationship between Initial v, x and y and projection angle).
Applications of Projectile Motion (1 of 4: Proving that two separate particles collide).
Projectile Motion (3 of 5: Defining the Acceleration, Velocity and Displacement Functions for x & y).
Projectile Motion (4 of 5: Finding max height using vertical velocity and displacement equations).
Projectile Motion (5 of 5: Finding Flight Time, Horizontal Range and Impact speed and angle).
Application of Projectile Motion (4 of 4: Proving that Path taken by projectile is a parabola).
Applications of Projectile Motion (2 of 4: Calculating V2, Collision Time & Place).
Applications of Projectile Motion (3 of 4: Finding the velocity the collision occurs at).
Harder Motion (2 of 2: Finding an expression for particle B to substitute time into to find x).
Harder Projectile Motion (1 of 5: Manipulating Trig Identities and finding time as a function of x).
Harder Projectile Motion (2 of 5: Substituting time expression to find velocity in terms of d).
Harder Projectile Motion (3 of 5: Finding what happens when theta approaches alpha and π/2).
Harder Projectile Motion (4 of 5: Finding a relationship between α & θ using Stationary Point).
Harder Projectile Motion (5 of 5: Using the second derivative to find the minimum value of θ).
Mechanics (1 of 7: Introduction to Forces and Newton's First Law and its relation to Mechanics).
Mechanics (2 of 7: Introduction to Newton's Second Law and Third Law and its relation to Mechanics).
Mechanics (3 of 7: Representing Physical Motion in mathematical terms).
Mechanics (4 of 7: Finding the angle subtended by the other line with the horizontal wall).
Mechanics (5 of 7: Resolving Forces to find the Horizontal forces acting on both strings).
Mechanics (6 of 7: Finding the Forces acting on the particle vertically).
Mechanics (7 of 7: Introductory Example to Mathematical Representation of Physical Motion).
Resisted Motion - Basic Example (1 of 2: Time as a function of Velocity).
Resisted Motion: Introductory Concepts.
Resisted Motion - Basic Example (2 of 2: Further Manipulation & Conclusions).
Resisted Motion - Harder Example (1 of 2: Maximum Height).
Resisted Motion - Harder Example (2 of 2: End of the journey).
Intro to Straight Line Motion (1 of 3: Overview of language).
Intro to Straight Line Motion (2 of 3: Unpacking a basic question).
Intro to Straight Line Motion (3 of 3: Interpreting the equations).
Simple Harmonic Motion Example Question (1 of 3: Determining period of motion).
Simple Harmonic Motion Example Question (2 of 3: Solving for time).
Simple Harmonic Motion Example Question (3 of 3: Using graph symmetry).
SHM - Other Centres of Motion (1 of 2: Rearranging with trigonometric identities).
SHM - Other Centres of Motion (2 of 2: Determining attributes from the equation).
Functions of Displacement (1 of 3: Basic Simple Harmonic Motion).
Functions of Displacement (2 of 3: SHM with different centre).
Functions of Displacement (3 of 3: Straight line motion example).
Equation of Path (1 of 4: Establishing the horizontal equations).
Equation of Path (2 of 4: Deriving the Cartesian equation).
Equation of Path (3 of 4: Finding horizontal range).
Equation of Path (4 of 4: Example question).
Simple Harmonic Motion v² Equation (1 of 2: Deriving the result).
Simple Harmonic Motion v² Equation (2 of 2: Example question).
HSC Tide Question (1 of 3: Proving the time equation).
HSC Tide Question (2 of 3: Solving for time).
HSC Tide Question (3 of 3: Leaving the harbour safely).
Intro to Mechanics (1 of 4: Mathematics & physics).
Intro to Mechanics (2 of 4: Equations & kinematics).
Intro to Mechanics (3 of 4: Simple harmonic motion - foundations).
Intro to Mechanics (4 of 4: Basic SHM example).
Simple Harmonic Motion example (1 of 3: Interpreting given data).
Simple Harmonic Motion example (2 of 3: Forming an equation).
Simple Harmonic Motion example (3 of 3: Identifying the time of a given displacement).
Acceleration in terms of displacement (1 of 2: Explanation).
Acceleration in terms of displacement (2 of 2: Worked example).
Simple Harmonic Velocity via Displacement (1 of 2: Equating forms of acceleration).
Simple Harmonic Velocity via Displacement (2 of 2: Worked example).
Objects in Equilibrium (1 of 4: Comparing forces with displacement).
Objects in Equilibrium (3 of 4: Balancing vertical forces).
Objects in Equilibrium (2 of 4: Using trigonometric relationships).
Objects in Equilibrium (4 of 4: Worked exam question).
Concurrent Forces - Non-Equilibrium (2 of 3: Worked example).
Concurrent Forces - Non-Equilibrium (1 of 3: Introduction).
Concurrent Forces - Non-Equilibrium (3 of 3: Finding magnitude & direction).
Horizontal Resisted Motion (1 of 3: Introduction).
Horizontal Resisted Motion (2 of 3: Velocity in terms of displacement).
Horizontal Resisted Motion (3 of 3: Locating eventual resting place).
Plane Braking Model (3 of 3: Resetting the time variable).
Plane Braking Model (2 of 3: Considering reverse thrust).
Plane Braking Model (1 of 3: Constant frictional force).
Vertical Resisted Motion (5 of 5: How long till it returns to the ground?).
Vertical Resisted Motion (4 of 5: Finding v = f(t) by integration).
Vertical Resisted Motion (3 of 5: Determining the maximum height).
Vertical Resisted Motion (2 of 5: Finding y = f(v) by integration).
Vertical Resisted Motion (1 of 5: Introduction).
Terminal Velocity (1 of 2: Balancing forces).
Terminal Velocity (2 of 2: Determining drop height).
Resisted Projectile Motion (1 of 4: Understanding horizontal motion).
Resisted Projectile Motion (2 of 4: Understanding vertical motion).
Resisted Projectile Motion (3 of 4: Finding cartesian equation).
Resisted Projectile Motion (4 of 4: Determining equations from first principles).
Quadratic Drag (1 of 3: Evaluating the drag coefficient).
Quadratic Drag (2 of 3: Investigating horizontal motion).
Quadratic Drag (3 of 3: Determining the angle of projection).
Proving simple harmonic motion (Exam Question 1 of 10).
Finding maximum speed of SHM (Exam Question 2 of 10).
Forces on a hanging object (Exam Question 5 of 10).
Mechanics of a falling object (Exam Question 10 of 10).