The Speedometer: Calculus Kinematics
Mastering displacement → velocity → acceleration through differentiation
EXAMINER TRAP ALERT
❌ WRONG: "At rest" means s = 0 (position is zero)
✓ CORRECT: "At rest" means v = 0 (velocity is zero)
📊 FREQUENCY: Very Common • 📉 MARK IMPACT: 2-3 marks
💡 HOW TO AVOID: Learn the motion ladder: s → v → a. "At rest" is about velocity, not position.
The Speedometer
Logic Track
📋 The Motion Ladder
Climb down the ladder by differentiating each time.
🎯 Key Concepts
- • Displacement (s): Position from fixed point O
- • Velocity (v): Rate of change of s → v = ds/dt
- • Acceleration (a): Rate of change of v → a = dv/dt
⚠️ Don't Confuse
📊 What You're Seeing
When t ≈ 0, notice how:
→ Particle momentarily at rest (v ≈ 0)
This is the turning point where direction changes!
Dynamic Solver: Motion Problem
📝 EXAM QUESTION (6 marks)
A particle moves in a straight line. Its displacement, s metres, from a fixed point O after t seconds is given by:
s = 2t³ − 9t² + 12t
Find the acceleration of the particle at the instant when it is at rest.
📚 Key Formulas (Higher Tier)
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