M5: Mechanics: Dynamics and Kinematics

Year 1 / ASYear 2 / A-Level All Boards (AQA, Edexcel, OCR, WJEC, CCEA) AQA

SUVAT equations, variable acceleration calculus, Newton's laws, friction, connected particles, projectiles.

Exam Board:

📋 Key Definitions and Core Concepts

Newton's 2nd Law: Resultant Force ΣF = ma (in Newtons).

Friction: F_max = μR where μ is coefficient of friction and R is normal reaction.

🔍 Key Principles & Specification Requirements

Calculus kinematics: r(t) → differentiate → v(t) → differentiate → a(t).
Projectiles: a_x = 0 (constant horizontal velocity u cos θ); a_y = -9.8 m/s².
Connected particles: formulate F = ma equation for each mass, solve simultaneously.

💡 Worked Example Question

Exam-Style Question

Question:

Mass 4 kg on a 30° rough slope with μ = 0.2. Find acceleration down slope.

Model Solution & Mark Scheme:

R = mg cos 30° = 4(9.8)(√3/2) = 33.95 N.
Friction = 0.2 × 33.95 = 6.79 N.
Weight down slope = 4(9.8) sin 30° = 19.6 N.
ΣF = 19.6 - 6.79 = 12.81 N => a = 12.81 / 4 = 3.20 m/s².

❓ Practice Questions & Mark Schemes

Q1: Velocity v(t) = 3t² - 12t + 9. Find displacement from t=0 to 3.

Show Model Answer

Answer: s(t) = t³ - 6t² + 9t. s(3) = 27 - 54 + 27 = 0 m.

Q2: Connected masses 3 kg and 5 kg over a pulley. Find acceleration.

Show Model Answer

Answer: 5g - T = 5a, T - 3g = 3a => 2g = 8a => a = 2.45 m/s².

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🎬 Video Resources

Mechanics: Dynamics and Kinematics - Overview -- YouTube Search
Mechanics: Dynamics and Kinematics - Exam Questions -- YouTube Search

📄 Past Papers & Exam Resources

AQA A-Level - Past Papers -- AQA
Edexcel A-Level - Past Papers -- Edexcel
OCR A-Level - Past Papers -- OCR

🔗 Further Reading & Resources

Physics & Maths Tutor -- Free notes, worksheets, and past paper questions by topic
Dr Frost Maths -- Free resources, slides, and interactive questions
BBC Bitesize -- BBC Bitesize revision resources

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