Time‑Speed‑Distance – Study Notes for Meghalaya Patwari / Lekhpal Exam
Why this topic?
Patwari’s duties often involve measuring distances between villages, planning travel routes, and estimating travel time. Mastering the basic time‑speed‑distance formulas will help you solve those questions quickly and accurately.
1. Simple Explanation
| Quantity | Symbol | Formula | What it Means |
|---|---|---|---|
| Distance | (D) | (D = S \times T) | Total ground covered. |
| Speed | (S) | (S = \dfrac{D}{T}) | Rate of travel (often in km/h). |
| Time | (T) | (T = \dfrac{D}{S}) | How long the travel takes. |
All three are inter‑related: knowing any two lets you compute the third.
Units
- Distance: km, m, ft
- Speed: km/h, m/s, ft/min
- Time: h, min, s
Convert units only when required (e.g., to compare speeds expressed in different units).
2. Key Points (Quick Reference)
| Concept | What to remember |
|---|---|
| Speed vs. Velocity | In exam problems we use speed (scalar). No direction needed. |
| Average Speed | (\displaystyle \text{Avg Speed} = \frac{\text{Total Distance}}{\text{Total Time}}). Use when a round trip or changing speeds. |
| Relative Speed | When two objects move towards/away from each other: (S_{\text{rel}} = S_1 + S_2) (towards) or (S_1 - S_2) (away). |
| Unit Conversions | 1 km/h = 1000 m / 3600 s ≈ 0.2778 m/s. 1 m/s = 3.6 km/h. |
| Common Mistakes | - Forgetting to convert units. - Mixing up “speed” and “velocity.” - Using wrong formula for average speed. |
| Time‑Distance Diagrams | Helpful for visualising relative motion. |
3. Worked Example
Problem
A Patwari walks from Village A to Village B, covering 20 km.
- He walks at a constant speed of 5 km/h for the first 10 km, then 8 km/h for the remaining 10 km.
- Find the total time taken.
- If he had walked at a constant speed of 6 km/h for the entire 20 km, how much time would he have saved?
Step‑by‑Step
| Part | Calculation | Result |
|---|---|---|
| 1. Time for first 10 km | (T_1 = \dfrac{D_1}{S_1} = \dfrac{10}{5} = 2) h | 2 h |
| 2. Time for next 10 km | (T_2 = \dfrac{D_2}{S_2} = \dfrac{10}{8} = 1.25) h | 1.25 h |
| 3. Total time | (T_{\text{total}} = T_1 + T_2 = 2 + 1.25 = 3.25) h | 3 h 15 min |
| 4. Constant speed 6 km/h | (T_{\text{const}} = \dfrac{20}{6} = 3.\bar{3}) h ≈ 3.33 h | ≈ 3 h 20 min |
| 5. Time saved | (\Delta T = T_{\text{const}} - T_{\text{total}} = 3.33 - 3.25 = 0.08) h ≈ 4.8 min | ≈ 5 min saved |
Interpretation
- The Patwari took 3 h 15 min to cover 20 km with two different speeds.
- If he had kept a steady 6 km/h, he would have taken about 3 h 20 min, so the variation actually saved him ~5 min.
- Tip: Always compute the exact time, then convert to minutes for clarity.
4. Quick Revision Summary
| Topic | Formula | Example Note |
|---|---|---|
| Distance | (D = S \times T) | Distance = Speed × Time. |
| Speed | (S = \dfrac{D}{T}) | Speed = Distance ÷ Time. |
| Time | (T = \dfrac{D}{S}) | Time = Distance ÷ Speed. |
| Average Speed | (\text{Avg} = \dfrac{D_{\text{total}}}{T_{\text{total}}}) | Use for round trips or varied speeds. |
| Relative Speed | (S_{\text{rel}} = S_1 + S_2) (towards) | When two people/vehicles meet. |
| Unit Conversion | 1 km/h = 0.2778 m/s | Convert only when speeds are expressed in different units. |
| Common Pitfalls | 1. Forget units 2. Mix speed/velocity 3. Wrong avg formula | Double‑check before final answer. |
Quick Practice Question (Try it!)
A