Time‑Speed‑Distance (TSD) – Quick Study Notes
For the Tripura Police Sub‑Inspector (SI) Quantitative Aptitude Paper
1. Simple Explanation
- Speed (or velocity) tells how fast an object is moving.
- Distance is the total ground covered (scalar).
- Time is the duration taken to cover that distance.
The three quantities are linked by a simple linear relationship:
speed = distance ÷ time
distance = speed × time
time = distance ÷ speed
Key idea – If you know any two of the three, you can find the third.
2. Key Points
| Concept | What it is | Typical Exam Question |
|---|---|---|
| Average speed | Total distance / total time | “Average speed of a bus that travels 60 km in 2 h and 40 km in 1.5 h.” |
| Relative speed | Speed of one object relative to another (often sum or difference) | “Two cars moving towards each other at 70 km/h and 50 km/h.” |
| Changing speeds | Break the journey into segments, compute each part, then combine | “A train goes 80 km at 60 km/h, then 120 km at 80 km/h.” |
| Units | Consistency matters (km, m, hr, min, sec). Convert when needed. | “A cyclist covers 12 km in 30 min.” |
| Speed vs. velocity | Speed is scalar (no direction). Velocity is vector. In SI paper, speed is usually meant. | “Average velocity of a person who walks 5 km north and 5 km south.” |
| Time–distance diagrams | Useful for visualizing relative motion | “Two trains start 200 km apart and meet after 3 h.” |
3. Important Formulas
| Formula | Variables | Units |
|---|---|---|
| (S = \dfrac{D}{T}) | Speed (S) | km/h, m/s |
| (D = S \times T) | Distance (D) | km, m |
| (T = \dfrac{D}{S}) | Time (T) | h, s |
| Average speed (multi‑segment) | (\displaystyle \text{Avg speed} = \frac{\text{Total distance}}{\text{Total time}}) | km/h |
| Relative speed (towards each other) | (S_{\text{rel}} = S_1 + S_2) | km/h |
| Relative speed (same direction) | (S_{\text{rel}} = | S_1 - S_2 |
| Time to meet | (T = \dfrac{\text{Initial distance}}{S_{\text{rel}}}) | h |
Tip: Always check units before plugging numbers.
4. Units & Conversions
| Unit | Symbol | Common Conversions |
|---|---|---|
| Kilometre | km | 1 km = 1000 m |
| Metre | m | 1 m = 100 cm |
| Hour | h | 1 h = 60 min = 3600 s |
| Minute | min | 1 min = 60 s |
| Speed | km/h or m/s | (1,\text{km/h} ≈ 0.2778,\text{m/s}) |
Always convert all distances to the same unit and all times to the same unit before using the formulas.
5. Types of Problems & Quick Strategies
| Problem Type | What to Look For | Quick Strategy |
|---|---|---|
| Single segment | One distance & one time (or speed). | Direct substitution in formula. |
| Multiple segments | Distinct speeds & distances. | Compute each segment’s time → sum times; compute total distance → divide. |
| Relative motion | Two objects moving (opposite or same direction). | Find relative speed first, then time or distance. |
| Average speed with stops | Journey broken into moving & stationary parts. | Treat stops as 0 speed; only moving parts add to distance and time. |
| **Unit conversion |