Quick Concept Summary
Every question in this topic returns to one triangle: distance = speed × time. The rest is choosing correct units and using relative speed when two moving objects are involved.
Unit Conversion
| Conversion | Rule |
|---|---|
| km/h to m/s | multiply by 5/18 |
| m/s to km/h | multiply by 18/5 |
Worked Examples
Example 1: Basic formula
A bus travels at 54 km/h for 2.5 hours.
Distance = 54 × 2.5 = 135 km
Example 2: Unit conversion
Convert 72 km/h to m/s.
72 × 5/18 = 20 m/s
Example 3: Equal-distance average speed
A person travels half the distance at 40 km/h and half at 60 km/h.
Average speed = 2ab/(a+b) = 2×40×60/100 = 48 km/h
Relative Speed
| Situation | Relative Speed |
|---|---|
| Same direction | Difference of speeds |
| Opposite direction | Sum of speeds |
Practice Questions
1. A car covers 180 km in 3 hours. Find speed. 2. Convert 15 m/s into km/h. 3. Two trains move at 50 km/h and 70 km/h in opposite directions. Find relative speed. 4. A man travels equal distances at 30 km/h and 45 km/h. Find average speed. 5. If speed increases by 25%, what happens to time for the same distance?
Common Mistakes
- Mixing km/h and m/s
- Taking simple average instead of harmonic average for equal distances
- Using sum instead of difference for same-direction motion
Revision Checklist
- [ ] Formula triangle
- [ ] Unit conversions
- [ ] Relative speed
- [ ] Average speed shortcut