Dosto, ye chapter Speed = Distance ÷ Time ke ek formula par khada hai. Isi se Trains (train khamba/platform/dusri train paar karti hai) aur Boats & Streams (nadi ki dhaara ke saath/against) ke sawal bhi ban jaate hain.
CET Group D mein isse 1–2 questions aate hain. Do cheezein ratt lo aur aadha chapter khatam: km/h → m/s ke liye × 5/18, aur train ka distance = train ki lambai + jo cheez paar kar rahi hai uski lambai.
Chapter 6 (Average) ka average speed = 2xy/(x+y) yahan bhi kaam aayega — dono chapters ek dusre se jude hain. Chalo shuru! 💪
1. Base Formula
Solved Example: 60 km, 45 minute mein → speed?
Step 1: 45 min = 45/60 = 3/4 ghanta (time hamesha ghante mein!)
Step 2: Speed = 60 ÷ 3/4 = 60 × 4/3 = 80 km/h ✓
2. Unit Conversion (⭐ har sawal mein lagta hai)
| km/h | m/s | km/h | m/s |
|---|---|---|---|
| 18 | 5 | 54 | 15 |
| 36 | 10 | 72 | 20 |
| 45 | 12.5 | 90 | 25 |
3. Speed–Time–Distance ka Rishta
- Distance same ho to speed aur time ULTE chalte hain (inverse) — speed ratio a:b ho to time ratio b:a.
- Time same ho to distance ∝ speed. Speed same ho to distance ∝ time.
Step 2: Time = 30 ÷ 6 = 5 ghante ✓ (speed badhi → time ghata)
4. Average Speed (Chapter 6 se jud gaya)
Solved Example: 60 km/h se jaata hai, 40 km/h se lautta hai → (2×60×40)/100 = 48 km/h ✓ (50 NAHI!)
5. TRAINS — ⭐ Sabse zaroori niyam
| Kya paar kar rahi hai | Distance |
|---|---|
| Khamba / aadmi / ped (point object) | Sirf train ki lambai |
| Platform / pul / tunnel | Train + platform ki lambai |
| Dusri train | Dono trains ki lambai |
Step 2: Speed = 150/15 = 10 m/s
Step 3: km/h mein = 10 × 18/5 = 36 km/h ✓
Step 2: Speed = 300/15 = 20 m/s = 72 km/h ✓
6. Relative Speed (do cheezein chal rahi hon)
Step 1: Relative speed = 60 + 40 = 100 km/h = 100 × 5/18 = 250/9 m/s
Step 2: Distance = 150 + 250 = 400 m
Step 3: Time = 400 ÷ 250/9 = 14.4 second ✓
7. BOATS & STREAMS (naav aur dhaara)
Naav ki speed (still water) = (down + up) ÷ 2 · Dhaara ki speed = (down − up) ÷ 2
24 km downstream jaane mein time = 24 ÷ 12 = 2 ghante ✓
Step 2: Dhaara = (15 − 9)/2 = 3 km/h ✓ (jodo ÷ 2 = naav, ghatao ÷ 2 = dhaara)
Dhyan: minute diye hon to ÷60 karke ghanta banao; metre-second diye hon to m/s mein hi raho.
Step 1: Distance = 180 + 270 = 450 m
Step 2: 450/20 = 22.5 m/s → × 18/5 = 81 km/h ✓
Same direction: relative = ghatao — 80 aur 60 km/h → 20 km/h (isliye bahut zyada time lagta hai).
Distance dono case mein dono lambaiyon ka jod hi rehta hai.
⚠️ Agar time barabar ho (doori nahi), tab simple average chalega — sawal dhyan se padho ki "same distance" hai ya "same time".
km/h → m/s: ×5/18 · ulta: ×18/5
Yaad rakhne ka tarika: m/s ka number chhota hota hai (18 km/h = 5 m/s), isliye chhota banane ke liye 5/18.
Khamba = sirf train · platform = train + platform
Khamba/aadmi/ped ki apni lambai zero maano. Ye ek line train ke aadhe sawal solve kar deti hai.
Naav = (D+U)/2 · Dhaara = (D−U)/2
Down aur up diya ho to jodo/2 se naav, ghatao/2 se dhaara. Poora Boats topic sirf isi ek line mein.
Speed 3:4 → Time 4:3
"Speed 25% badha di to kitna time bachega?" — speed 5:4 → time 4:5 → 20% time bachega (Ch 4 + Ch 5 ka mel!).
Aamne-saamne = jodo · peechha = ghatao
Ulti disha mein trains jaldi cross hoti hain (speed jud jati hai), same disha mein bahut der lagti hai (speed ghat jati hai).
| Cheez | Formula / Value |
|---|---|
| Speed · Distance · Time | D/T · S×T · D/S |
| km/h → m/s · m/s → km/h | ×5/18 · ×18/5 |
| 36 · 54 · 72 km/h | 10 · 15 · 20 m/s |
| Khamba paar | Distance = train ki lambai |
| Platform/pul paar | Distance = train + platform |
| Do train paar | Distance = dono ki lambai |
| Opposite direction | Relative = a + b |
| Same direction | Relative = a − b |
| Downstream · Upstream | b+s · b−s |
| Naav · Dhaara | (D+U)/2 · (D−U)/2 |
| Average speed (same doori) | 2xy/(x+y) |
| Distance same | Speed & time ulta |
Q1. A car covers 60 km in 45 minutes. Its speed is:
Q2. 72 km/h is equal to:
Q3. 25 m/s is equal to:
Q4. A train 150 m long crosses a pole in 15 seconds. Its speed is:
Q5. A train 200 m long crosses a platform 100 m long in 15 seconds. Its speed is:
Q6. Two trains of lengths 150 m and 250 m run in opposite directions at 60 km/h and 40 km/h. Time taken to cross each other is:
Q7. The speed of a boat in still water is 10 km/h and the speed of the stream is 2 km/h. Its downstream speed is:
Q8. A boat goes downstream at 15 km/h and upstream at 9 km/h. The speed of the stream is:
Q9. A man covers 120 km in 3 hours. At the same speed, the time taken to cover 200 km is:
Q10. A train 180 m long crosses a bridge 270 m long in 20 seconds. Its speed is:
Q11. A man walking at 5 km/h covers a distance in 6 hours. At 6 km/h, he will cover the same distance in:
Q12. Two trains run in the same direction at 80 km/h and 60 km/h. Their relative speed is:
Q13. A boat whose speed in still water is 10 km/h goes 24 km downstream in a stream flowing at 2 km/h. The time taken is:
Q14. A man goes to a place at 60 km/h and returns along the same route at 40 km/h. His average speed for the whole journey is:
Ek formula — Speed = Distance ÷ Time — aur do conversions: km/h → m/s ×5/18, ulta ×18/5. Train ke sawal mein sabse zaroori: khambe par distance = sirf train ki lambai, platform/pul par = train + platform, do trains par = dono ki lambai. Relative speed: ulti disha mein jodo, ek hi disha mein ghatao. Boats mein down = b+s, up = b−s, aur ulta nikalna ho to naav = (D+U)/2, dhaara = (D−U)/2. Barabar doori ka average speed 2xy/(x+y) hai — 60 aur 40 ka jawab 48, 50 nahi! 🚀