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IGCSE Maths: Speed, Distance & Time — Notes

IGCSE Mathematics — Speed, Distance & Time

Complete notes with worked examples, graphs, and self‑test quizzes.

1) Core Formula

Speed = Distance ÷ Time   •   Distance = Speed × Time   •   Time = Distance ÷ Speed

Keep units consistent before calculating.

Example 1

A car travels 150 km in 3 hours. Find average speed.

Solution Speed = 150 ÷ 3 = 50 km/h.

Self‑Test 1

  1. A cyclist travels 60 km in 4 hours. Average speed?
  2. A runner runs at 12 km/h for 45 minutes. How far?

2) Unit Conversions

  • 1 km = 1000 m, 1 hour = 3600 s
  • km/h → m/s: multiply by 5/18
  • m/s → km/h: multiply by 18/5

Example 2

Convert 72 km/h to m/s → 72 × 5/18 = 20 m/s.

Self‑Test 2

  1. Convert 54 km/h to m/s.
  2. Convert 15 m/s to km/h.

3) Average Speed

Average speed = Total distance ÷ Total time

Do not average speeds directly.

Example 3

Annette cycles 30 km in 2 h, rests 0.5 h, then 40 km in 2.5 h.

Solution Distance = 70 km, Time = 5 h → Average speed = 14 km/h.

Self‑Test 3

A car travels 120 km at 60 km/h, then 180 km at 90 km/h. Find overall average speed.

4) Distance–Time Graphs

Gradient = speed. Horizontal line = stationary. Steeper = faster.

Distance-Time Graph Example

Example 4: 40 km in 1 h, rest 0.5 h, 30 km in 1.5 h. Total distance 70 km, total time 3 h, average ≈ 23.3 km/h.

Self‑Test 4

Plot: 20 km in 30 min → rest 15 min → 10 km in 30 min. Find average speed.

5) Speed–Time Graphs

Gradient = acceleration. Area under graph = distance.

Speed-Time Graph Example

Example 5: Accelerate to 20 m/s in 10 s, travel 15 s, stop in 5 s. Acceleration = 2 m/s², Distance = 450 m.

Self‑Test 5

  1. Decelerate from 30 m/s to 0 in 15 s. Find deceleration.
  2. Find distance travelled during this time.

6) Bearings & Trigonometry

Bearings measured clockwise from North (3 digits).

Example 6

Ship sails 60 km east then 80 km north → Distance = √(60²+80²) = 100 km.

Self‑Test 6

Plane flies 100 km north then 240 km east. Find distance from start and the bearing from start.

Answer Key (Self‑Tests)

Show/Hide Answers
  1. Self‑Test 1: (1) 15 km/h. (2) 9 km.
  2. Self‑Test 2: (1) 15 m/s. (2) 54 km/h.
  3. Self‑Test 3: Time = 2 h + 2 h = 4 h, Distance = 300 km → 75 km/h.
  4. Self‑Test 4: Distance = 30 km, Time = 1.25 h → 24 km/h.
  5. Self‑Test 5: (1) 2 m/s² deceleration. (2) ½ × 15 × 30 = 225 m.
  6. Self‑Test 6: Distance = √(100² + 240²) = 260 km. Bearing = arctan(240/100) ≈ 067°.
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