Introduction
When a particle moves along a straight line with constant (uniform) acceleration, the relationship between displacement, velocity, acceleration, and time can be captured by a concise set of formulae. These are among the most heavily tested results in the 9709 Mechanics paper: they appear in straightforward single-particle problems and also in more demanding questions where two or more particles move simultaneously, requiring you to form and solve a system of equations. Mastery of these formulae — and knowing which one to apply first — is essential for efficiency under exam conditions.
Core Concept
Suppose a particle travels in a straight line. We define the following quantities, all measured from a fixed reference point and direction (positive direction must be stated or assumed):
| Symbol | Meaning | SI Unit |
|---|---|---|
| displacement from starting position | m | |
| initial velocity | m s | |
| final velocity (at time ) | m s | |
| acceleration (constant) | m s | |
| time elapsed | s |
The key condition for all five formulae is that is constant throughout the interval considered. If acceleration varies, calculus-based methods (differentiation/integration) must be used instead.
Sign convention: Choose a positive direction at the start of every problem. Velocities, accelerations, and displacements in the opposite direction are then negative. Consistency here prevents the most common errors.
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