Speed Distance Master - Quick Revision
Speed Distance Master - Quick Revision
One-Liners
- Speed = Distance ÷ Time; always check units first.
- Average speed ≠ (u + v)/2 unless distance is same both ways.
- Upstream speed = Boat – Stream; downstream = Boat + Stream.
- Relative speed same-direction: subtract; opposite: add.
- 1 km/h = 5⁄18 m/s; 1 m/s = 18⁄5 km/h.
- Two objects meet: distance gap = (relative speed) × time.
- Train crossing pole: distance = train length only.
- Train crossing platform: distance = train + platform length.
- Circular track nth meet: faster gains n laps.
- Stoppage time = (Normal speed – Travel speed) ÷ Normal speed × 60 min.
- If speed ↑ 3×, time ↓ 1⁄3 for fixed distance.
- Total distance ÷ total time = actual average speed.
- Escalator steps = (man speed ± escalator speed) × time.
- Speed ratios a : b give time ratios b : a.
- Meeting point distance from start ∝ speed when time same.
- Races: beaten distance = (faster speed – slower speed) × time.
- km/h → m/s shortcut: halve, then ÷ 3 (≈ 5⁄18).
- Time gap overtaking = head-start distance ÷ relative speed.
- Clock hands 90°: 2 times/hour, 44 times/day.
- 1 mph ≈ 1.6 km/h; 1 knot ≈ 1.85 km/h.
| Formula |
Use |
| Speed = Distance / Time |
Basic triplet conversion |
| Average speed = 2uv / (u + v) |
Same-distance up & down |
| Relative speed (opposite) = u + v |
Two bodies towards each other |
| Relative speed (same) = |
u – v |
| Boat downstream = b + s |
Stream aiding |
| Boat upstream = b – s |
Stream opposing |
| Time with stoppage = D / (S – s) |
S normal, s travel speed |
| Circular 1st meet = C / |
v₁ – v₂ |
| Train time = (Lₜ + Lₒ) / v |
Lₜ train, Lₒ object length |
| km/h → m/s × 5⁄18 |
Unit conversion |
Memory Tricks
- USD – Units Same Divide: distance & time units must match before you divide.
- “Boat SAM” – Stream Aids (Adds) Motion; upstream Minus.
- “TOPS” – Train Over Pole = Single length (train only).
- “RED” – Relative speed: Enemies Definitely add, Siblings subtract.
- “2-2-5” – km/h → m/s: two-two-five (5/18) and reverse eighteen-five.
Common Errors
| Error |
Correct |
| Using (u + v)/2 for average speed |
Use total distance ÷ total time |
| Forgetting to add train length when crossing bridge |
Distance = train + bridge |
| Adding speeds when running in same direction |
Subtract for relative speed |
| Taking m/s → km/h × 5/18 |
Must × 18/5 |
| Ignoring unit consistency |
Convert all to km-h or m-s before formula |
5 Quick MCQs
1. A 200 m train at 54 km/h crosses a pole in ___ s.
Answer: 13.33 s (200 ÷ 15 m/s)
2. Ramesh beats Suresh by 40 m in a 200 m race; if Ramesh runs 200 m, how much will he beat Suresh in 400 m?
Answer: 80 m
3. A boat 15 km/h in still water faces 5 km/h current. Downstream speed is ___ km/h.
Answer: 20 km/h
4. A car travels 40 km at 20 km/h & 60 km at 30 km/h. Average speed is ___ km/h.
Answer: 24 km/h
5. Two walkers start 14 km apart, meet in 2 h with speeds 3 & 4 km/h. They walk ___ direction.
Answer: Opposite (sum 7 km/h)
BETA
