Quick Reference Formulas
Unit Conversions
| 🔄 Conversion Type | Formula | Example |
|---|---|---|
| 🚄 km/hr to m/s Convert speed from kilometers per hour to meters per second | a km/hr=a× (18/5) m/s | 36 km/hr = 10 m/s |
| 🚆 m/s to km/hr Convert speed from meters per second to kilometers per hour | a m/s=a×( 5/18 )km/hr | 15 m/s = 54 km/hr |
Time Calculations for Passing Objects
| 🎯 Scenario | 📏 Distance to Cover | ⏱️ Time Formula |
|---|---|---|
| 🚉 Passing a pole/person/signal | Length of train (l meters) | Time = l/speed |
| 🌉 Passing a stationary object | Train length + Object length (l + b meters) | Time = (l + b)/speed |
Relative Speed Concepts
When two trains move in same direction at speeds uu m/s and vv m/s
Contents
| 🔀 Direction of Movement | 🎯 Objects | ⚡ Relative Speed Formula |
|---|---|---|
| ➡️➡️ Same Direction | Speed u m/s and v m/s (where u > v) | (u – v) m/s |
| ⬅️➡️ Opposite Directions | Speed u m/s and v m/s | (u + v) m/s |
Train Crossing Scenarios
| 🚂 Situation | 📐 Parameters | ⏰ Time Formula |
|---|---|---|
| ⬅️🚄➡️🚆 Opposite directions | Trains: a m and b m long Speeds: u m/s and v m/s | Time = (a + b)/(u + v) seconds |
| ➡️🚄🚆➡️ Same direction | Trains: a m and b m long Speeds: u m/s and v m/s | Time = (a + b)/(u – v)seconds |
Speed Ratio Formula
| 🏁 Special Case | 📊 Condition | 🔢 Speed Ratio |
|---|---|---|
| 🔄 Trains starting simultaneously | Start from points A and B towards each other After crossing: Train A takes a sec to reach B Train B takes b sec to reach A | A’s speed : B’s speed = √b : √a |
