Vectors

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A2 Maths – Mechanics – Vectors in Mechanics

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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8A Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Further Kinematics 1 • Vector Motion • Mech2 Ex8A • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 1-9✦

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 660a: Determine the speed of a particle given its velocity vector.
• 660b: Determine the angle of direction associated with a velocity vector.
• 660c: Determine the bearing of a moving particle given two displacements.
• 660d: Use the formula textbfr_B = textbfr_A + textbfvt to determine the position of a particle after a given time or vice versa.
• 660e: Determine the velocity or speed of a particle given a displacement vector textbfr_B = textbfr_A + textbfvt
• 660f: Use the formula textbfr_B = textbfr_A + textbfvt to determine the velocity or speed of a particle given two displacements.
• 660g: Determine a vector for the displacement of a particle in terms of the time t, given two positions of the particle.
• 660h: Determine the time at which two particles meet, given their initial displacements and velocities.
• 660i: Determine the time at which a particle is at a cardinal direction relative to a fixed point.
• 660j: Determine the times at which a particle is a given distance from a fixed point, given its displacement in terms of the time t
• 660k: Determine the times at which two particles are at a given distance apart, given their initial displacements and velocities.
• 660l: Determine the time at which a particle is at a cardinal direction relative to another, given their displacement vectors in terms of time t
• 660m: Determine the speed of a particle, involving an unknown constant, when it is at a cardinal direction relative to another particle. (not yet active)
• 661a: Use textbfF = mtextbfa to find the magnitude of a force given an acceleration vector or vice versa. (not yet active)
• 661b: Use the formula textbfv = textbfu + textbfat with vectors to find the acceleration. (not yet active)
• 661c: Use the formula textbfv = textbfu + textbfat with vectors to find a velocity as a function of time t (not yet active)
• 661d: Use the formula textbfv = textbfu + textbfat with vectors to find a speed at a given time. (not yet active)
• 661e: Use the formula textbfr = textbfut + 1/2textbfat² with vectors to find a position vector at a given time. (not yet active)
• 661f: Use the formula textbfr = textbfut + 1/2textbfat² with vectors to find the distance from a starting point at a given time. (not yet active)
• 661g: Calculate a vector for velocity to determine the time when a particle is moving in a particular cardinal direction. (not yet active)
• 661h: Determine the value of a constant in a velocity vector given the magnitude of a force. (not yet active)
• 660: Exam Practice: Vector calculations for displacement or velocity with constant velocity
• 661: Exam Practice: Vector calculations given a constant acceleration vector

Other Videos

Vectors Using i and j notation

Courtesy of Maths Genie (mainly v = u + at with vectors)

Velocity Vectors (1) – Calculating Speed : ExamSolutions Maths Revision

Velocity Vectors – Calculating Speed (Exercise) : ExamSolutions Maths Revision

Velocity Vectors (2) – Calculating velocity given speed and direction : ExamSolutions Maths Revision

Velocity Vectors (2) (Example) Calculating velocity given speed and direction : ExamSolutions

Velocity Vectors (3) Finding a position vector after time t : ExamSolutions Maths Revision

Velocity Vectors (4) – Velocity as a rate of change of position : ExamSolutions Maths Revision

Exam Solutions videos and worked examples

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• The Chalk Face Lord Franklin
• The Chalkface
  • Lord Franklin Vectors: PDF

Worksheets

• Mathshelper (Jon Stone)
  • Kinematics In 2D Worksheet
• MathedUp
  • Kinematics in 2D: Questions · Challenge · Answers
• MadAsMaths (T. Madas)
  • Vectors in Mechanics (M1) With Acceleration Q4–6, 8, 9, 12, 13, 15–21; Without Acceleration Q1–23; Various Q1 (difficulty 2–4 of 5)

Exam Practice

• Exam Solutions Section with PPQs and Attached Video Tutorials
• PMT PPQ Booklet from Old M1 Questions

A2 Maths – Mechanics – Projectiles with Vectors

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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8B Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Further Kinematics 2 • Vector Projectiles – regular method is better! • Mech2 Ex8B • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 10-12✦

Extra Questions

• Dr Frost Questions (only one 2-part question)

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 654r: Use vectors to solve projectile motion problems.
• 654: Exam Practice: Projectile motion in 2D

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Exam Practice

• PMT Q2 from PPQ Booklet from Old M2

A2 Maths – Mechanics – Variable Acceleration in One Dimension

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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8C Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Further Kinematics 3 • Variable Acceleration in One Dimension – revisited • Mech2 Ex8C • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 13-15✦

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 558a: Use differentiation to find an expression for the velocity or the acceleration of a particle.
• 558b: Determine when a particle is instantaneously at rest, given an expression for the velocity.
• 558c: Determine when a particle is instantaneously at rest, given an expression for the displacement.
• 558d: Use differentiation once to find the velocity or acceleration of a particle at a given instant.
• 558e: Use differentiation twice to find the acceleration of a particle at a given instant.
• 558f: Use integration once to find an expression for the displacement or the velocity of a particle.
• 558g: Use integration twice to find an expression for the displacement of a particle.
• 558h: Use integration once find the displacement or the velocity of a particle at a given instant.
• 558i: Use integration twice find the displacement of a particle at a given instant.
• 558j: Show that the displacement or velocity is always positive.
• 558k: Sketch a velocity-time graph given an expression for the displacement.
• 558l: Determine the maximum displacement or velocity reached of a particle.
• 558m: Determine the distance travelled where the velocity changes between positive and negative throughout the journey.
• 558n: Solve problems involving variable acceleration where two objects meet.
• 558o: Use a velocity-time graph or other sets of data to determine multiple unknown coefficients for a quadratic expression for velocity.
• 558p: Derive the constant acceleration formulae using calculus.
• 558: Exam Practice: Calculus in kinematics for motion in a straight line, e.g. v = dr/dt, in 1 dimension

Other Videos

Kinematics : Linear Motion with Variable Acceleration : ExamSolutions Maths Revision

Linear Motion with Variable Acceleration ( Example) : ExamSolutions Maths Revision

Linear Motion with Variable Acceleration (Example) : ExamSolutions Maths Revision

Exam Solutions videos and worked examples

I Will Derive!

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Exam Practice

• Exam Solutions Section with PPQs and Attached Video Tutorials

A2 Maths – Mechanics – Differentiating Vectors

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

8D Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Further Kinematics 4 • Differentiating Vectors • Mech2 Ex8D • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 16-17✦

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 662a: Solve problems involving F=ma where the force and acceleration are vectors. (not yet active)
• 662b: Differentiate once to find the velocity or acceleration (vector) of a particle at a particular time. (not yet active)
• 662c: Differentiate twice to find the acceleration (vector) of a particle at a particular time. (not yet active)
• 662e: Use a vector for velocity to determine the time when a particle is moving in a particular direction. (not yet active)
• 662f: Use a vector for velocity to determine the time when a particle is moving at a given speed. (not yet active)
• 662: Exam Practice: Vector calculations for displacement or velocity with variable acceleration

Other Videos

Kinematics : Linear Motion with Variable Acceleration – Summary Example : ExamSolutions

Variable Acceleration Vectors (1) – Differentiation Methods : ExamSolutions Maths Revision

Exam Solutions video and worked example

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheets

• MadAsMaths (T. Madas)
  • Kinematics Using Calculus (M1/M2) Vector Form Q1, 2, 4–6 (difficulty 2–3 of 5)
  • Vectors in Mechanics (M1) With Acceleration Q14 (difficulty 4 of 5)

A2 Maths – Mechanics – Integrating Vectors

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

8E Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Further Kinematics 5 • Integrating Vectors • Mech2 Ex8E • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 18-22✦

Exam Practice

• Exam Practice

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 662d: Integrate to determine the displacement at time t of a particle given its velocity and initial displacement. (not yet active)
• 662: Exam Practice: Vector calculations for displacement or velocity with variable acceleration

Further Practice

• Practise Questions

Other Videos

Variable Acceleration Vectors (2) – Integration Methods : ExamSolutions Maths Revision

Exam Solutions worked example

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheets

• MadAsMaths (T. Madas)
  • Kinematics Using Calculus (M1/M2) Vector Form Q3, 7, 8 (difficulty 2–4 of 5)

Exam Practice

• Exam Solutions Section with PPQs and Attached Video Tutorials

External Whole Topic Past Paper Style Questions

• WW Dr Frost Style QQQs (Version 1) Word Doc, PDF (Q’s Only) or PDF (Q’s & Sol.)
• WW Dr Frost Style QQQs (Version 2) Word Doc, PDF (Q’s Only) or PDF (Q’s & Sol.)
• Jethwa Maths Starter Activity
• PMT
  • AQA Kinematics & MS
  • Edexcel
    • Kinematics
    • Kinematics – Problems with Vectors 1 · 2
  • OCR Non-Uniform Acceleration
  • OCR MEI Motion in 2 Dimensions
  • Cheat Sheet

Other Whole Topic Resources

•  Lucyjc1612 Summary Poster (Vectors)
• Andy Lutwyche: Erica’s Errors

Worksheets

• Mathshelper (Jon Stone)
  • Vector Motion 1 · 2
• MathedUp
  • Variable acceleration: Questions · Challenge · Answers
• Maths Genie
  • Further Kinematics: Questions · Solutions · Lesson · Topic page
• Mathsaurus (Kevin Olding)
  • Kinematics (exam questions)
• Naiker Maths
  • Further Kinematics: Exam Qs 2005–11 · Mark scheme
• Physics & Maths Tutor
  • Kinematics: Problems in Calculus: Questions 2021–24 · Mark scheme · Model answers

Activities

• MEI
  • MEI teaching notes, misconceptions & prompts: Kinematics✦