Contents
1. Key Definitions
Total path length travelled — scalar (no direction).
Straight-line distance from start to finish in a specified direction — vector.
Distance travelled per unit time — scalar. Average speed = total distance ÷ total time.
Displacement per unit time in a stated direction — vector.
Rate of change of velocity — vector. a = (v − u) ÷ t, unit m/s².
A negative acceleration (deceleration) means velocity is decreasing in the positive direction.
2. Motion Graphs
Distance-time graph
| Shape of line | Meaning |
|---|---|
| Horizontal line | Object is stationary (distance not changing) |
| Straight line with positive gradient | Constant speed |
| Curved line (gradient increasing) | Accelerating |
| Curved line (gradient decreasing) | Decelerating |
Gradient of a distance-time graph = speed.
Speed-time graph
| Shape of line | Meaning |
|---|---|
| Horizontal line | Constant speed (zero acceleration) |
| Straight line with positive gradient | Uniform acceleration |
| Straight line with negative gradient | Uniform deceleration |
| Curved line | Non-uniform (changing) acceleration |
Gradient of a speed-time graph = acceleration.
Area under a speed-time graph = distance travelled.
For a trapezium shape: area = ½ × (sum of parallel sides) × height. For a triangle: area = ½ × base × height. Always check the axes — time is usually x, speed is y.
3. Calculating Motion
A car accelerates from rest to 24 m/s in 8 s. Find (a) acceleration, (b) distance travelled.
(a) a = (v − u) ÷ t = (24 − 0) ÷ 8 = 3 m/s²
(b) distance = ½(u + v)t = ½ × (0 + 24) × 8 = 96 m
4. Free Fall and Terminal Velocity
In free fall (no air resistance), all objects accelerate downward at g = 10 m/s² regardless of mass. This is because gravitational force is proportional to mass, but so is the resistance to acceleration (inertia).
Terminal velocity
When an object falls through a fluid (air or liquid), air resistance increases as speed increases. Eventually, air resistance equals the weight of the object — the resultant force is zero and the object falls at constant (terminal) velocity.
| Stage | Forces | Motion |
|---|---|---|
| Initial fall | Weight > air resistance | Accelerating downward |
| Approaching terminal v | Weight > air resistance (smaller gap) | Still accelerating, but less |
| Terminal velocity | Weight = air resistance | Constant velocity (zero acceleration) |
At terminal velocity, students write "there is no force on the object". Wrong — there are still two forces (weight and air resistance). They are equal and opposite, so the resultant is zero and acceleration is zero.
- Velocity-time graph: gradient = acceleration; area under graph = displacement
- Distance-time graph: gradient = speed; curve = accelerating; flat = stationary
- Free fall: a = g = 10 m/s2 downward (O-Level value). Air resistance neglected.
- Average speed = total distance / total time (NOT displacement)
- If v-t graph goes below x-axis, object is moving in opposite direction
5. Common Exam Traps
On a distance-time graph, gradient = speed. On a speed-time graph, gradient = acceleration AND area = distance. Students regularly mix these up.
If a question says "starts from rest" or "released from rest", u = 0. Always substitute u = 0 first, then solve.
Deceleration is not a negative quantity by itself — it depends on the direction chosen as positive. State clearly: "the acceleration is −3 m/s², meaning the car is decelerating at 3 m/s²."
Key Terms — Flashcard Review
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🎯 Practice Quiz — Test Yourself
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Original study notes for Singapore students. Not affiliated with MOE, SEAB or Cambridge. Use alongside your school notes and official syllabus documents.