Distance = Speed × Time

🎯 Learning Objective

Use D = S × T fluently and convert km/h ↔ m/s with the 5/18 factor.

💡 Concept

• Distance = Speed × Time; S = D/T; T = D/S — one triangle, three formulas
• km/h → m/s: multiply by 5/18 (72 km/h = 20 m/s)
• m/s → km/h: multiply by 18/5 (25 m/s = 90 km/h)
• Make units consistent BEFORE calculating — metres with seconds, km with hours
• Same distance → speed and time are inversely proportional

🧮 Key Formulas

D = S × T

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km/h → m/s: × 5/18

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m/s → km/h: × 18/5

✏️ Easy Example

Q. A car runs at 60 km/h for 2.5 hours. How far does it travel?

1. D = S × T
2. = 60 × 2.5

Answer: 150 km

🇮🇳 Real-Life Example

Google Maps saying 'Airport — 30 km, 45 min' has simply divided distance by an average speed of 40 km/h. You run D = S × T every time you check an ETA.

📝 Exam-Level Example

Q. A cyclist covers 45 km at 15 km/h; a bike covers the same distance at 45 km/h. How much time does the bike save?

1. Cycle: 45 ÷ 15 = 3 h
2. Bike: 45 ÷ 45 = 1 h
3. Saved = 3 − 1

Answer: 2 hours

📝 Exam-Level Example

Q. A bus covers 180 km in 2 hours. Find its speed in m/s.

1. Speed = 180 ÷ 2 = 90 km/h
2. m/s = 90 × 5/18

Answer: 25 m/s

🪄 Memory Trick

m/s is always the smaller number — so going to m/s, multiply by the smaller fraction 5/18. Pairs: 36↔10, 54↔15, 72↔20, 90↔25, 108↔30.

⚠️ Common Mistakes

• ❌ Mixing km with seconds without converting
• ❌ Using 18/5 when going km/h → m/s

🏆 Exam Tips

• ✅ Memorise the conversion pairs from 36↔10 up to 108↔30
• ✅ Draw the D-S-T triangle whenever you feel confused

📌 Summary

• D = S × T — one formula, three forms
• km/h → m/s: × 5/18
• m/s → km/h: × 18/5
• Fix units before touching numbers