1.2 Motion (Core)
1.2.1 Learning Objective
Define acceleration as the change in velocity per unit time, recall and use the equation a = Δv / Δt, and apply the related kinematic concepts and equations to solve motion problems.
1.2.2 Key Concepts
- Speed – scalar quantity (m s⁻¹) that tells how fast an object moves.
- Velocity – vector quantity (m s⁻¹) that includes both speed and direction.
- Acceleration – vector quantity (m s⁻²) that describes the rate of change of velocity. It may be a change in speed, a change in direction, or both.
- Sign convention – In the syllabus a positive acceleration means the speed is increasing in the chosen positive direction; a negative acceleration (often called deceleration) means the speed is decreasing.
- Scalars vs. Vectors – Scalars have magnitude only; vectors have magnitude and direction.
- Free‑fall – motion under the influence of gravity alone; acceleration g ≈ 9.8 m s⁻² downwards (taken as negative if upward is chosen as positive).
- Graphical interpretation – distance‑time and speed‑time graphs are essential tools for analysing motion.
1.2.3 Definitions & Fundamental Equations
| Quantity | Symbol | Definition | Equation | Units |
|---|
| Speed | v | distance travelled per unit time (scalar) | v = s / t | m s⁻¹ |
| Velocity | →v | speed with a specified direction (vector) | →v = Δ→s / Δt | m s⁻¹ |
| Acceleration | →a | change in velocity per unit time (vector) | →a = Δ→v / Δt | m s⁻² |
| Free‑fall acceleration | g | constant acceleration of a body falling under gravity | g ≈ 9.8 m s⁻² (downwards) | m s⁻² |
Related Kinematic Equations (constant acceleration)