Motion
Scalar and vector quantities
Scalar quantities have magnitude only: distance, speed, time, mass, temperature. Vector quantities have both magnitude and direction: displacement, velocity, acceleration, force.
A common CCEA question asks you to distinguish between distance and displacement, or speed and velocity — always mention direction for vectors.
Key equations
| Quantity | Equation | Units |
|---|---|---|
| Speed | v = d / t | m/s |
| Average velocity | v = Δs / Δt | m/s |
| Acceleration | a = (v − u) / t | m/s² |
| Displacement (uniform a) | s = ut + ½at² | m |
| v² = u² + 2as (uniform a) | — | — |
Where: u = initial velocity, v = final velocity, a = acceleration, s = displacement, t = time.
Note: The CCEA data sheet provides v = u + at, s = ut + ½at², v² = u² + 2as. You MUST quote the correct equation and show substitution for method marks.
Distance–time graphs
- Gradient = speed (or velocity if direction matters).
- Horizontal line → object is stationary.
- Straight sloping line → constant speed.
- Curve → changing speed (accelerating or decelerating).
- A steeper gradient means greater speed.
Velocity–time graphs
- Gradient = acceleration (a = Δv / Δt).
- Area under the graph = displacement (distance travelled if no direction change).
- Horizontal line → constant velocity, zero acceleration.
- Straight line rising → uniform acceleration.
- Straight line falling → uniform deceleration.
- Curve → non-uniform acceleration.
For CCEA 6-mark extended questions, you may be asked to describe the motion shown in a v-t graph segment by segment: state velocity at start and end, sign of gradient, and what this means physically.
Acceleration due to gravity
Near Earth's surface, g ≈ 9.8 m/s² (CCEA data sheet value). In free fall (ignoring air resistance) all objects accelerate at g downward regardless of mass. CCEA questions often use g = 10 m/s² for non-calculator sections.
Terminal velocity
As a falling object speeds up, air resistance (drag) increases. When drag equals weight, net force = 0, acceleration = 0 and the object falls at terminal velocity (covered in more depth in U1.2).
Common CCEA mistakes
- Not giving units for every numerical answer — mark schemes always require units.
- Confusing gradient and area on v-t graphs — gradient gives acceleration, area gives displacement.
- Forgetting to include direction when asked for velocity or acceleration.
- Using g = 9.81 when the question says 9.8 or 10 — use the value given or the CCEA data sheet value.
- Not squaring in v² = u² + 2as — a very common arithmetic slip.
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