Define acceleration as change in velocity per unit time; recall and use the equation a = Δv / Δt

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

QuantitySymbolDefinitionEquationUnits
Speedvdistance travelled per unit time (scalar)v = s / tm s⁻¹
Velocity→vspeed with a specified direction (vector)→v = Δ→s / Δtm s⁻¹
Acceleration→achange in velocity per unit time (vector)→a = Δ→v / Δtm s⁻²
Free‑fall accelerationgconstant acceleration of a body falling under gravityg ≈ 9.8 m s⁻² (downwards)m s⁻²

Related Kinematic Equations (constant acceleration)

  • v = u + at