Time‑Speed‑Distance – Study Notes
(For Punjab Patwari / Lekhpal Quantitative Aptitude)
1. Simple Explanation
The time‑speed‑distance (T‑S‑D) relation is the most basic concept in kinematics.
It tells you how far an object travels (distance, d) when you know its speed (rate of motion, s) and the time it moves (time, t).
Formula
[ \boxed{d ;=; s \times t} ]
- d – distance (km, m, miles, etc.)
- s – speed / velocity (km/h, m/s, mph, etc.)
- t – time (h, min, s, etc.)
If you have any two of the three variables, you can find the third by rearranging the formula:
| Known | Unknown | Formula |
|---|---|---|
| d & t | s | (s = \dfrac{d}{t}) |
| d & s | t | (t = \dfrac{d}{s}) |
| s & t | d | (d = s \times t) |
Tip: Keep the units consistent. If speed is in km/h, time must be in hours to get distance in km.
2. Key Points
| # | Concept | Why It Matters |
|---|---|---|
| 1 | Rate of Motion | Speed is distance per unit time. Knowing the rate allows you to compute how far an object will travel. |
| 2 | Unit Consistency | Mixing units (e.g., km with minutes) leads to wrong answers. Convert first if needed. |
| 3 | Average vs Instantaneous Speed | In most exam questions, speed is taken as average speed unless stated otherwise. |
| 4 | Rearranging the Formula | Practice switching between (d = st), (s = d/t), (t = d/s). |
| 5 | Multiple Segments | For journeys with different speeds or times, treat each segment separately, then sum distances or times. |
| 6 | Common Traps | - Forgetting to divide by 60 when converting minutes to hours. - Using the wrong formula (e.g., (d = s/t)). |
| 7 | Word Problems | Identify the given variables, convert units, apply the right formula, and double‑check dimensions. |
3. Worked Example
Problem
A truck travels from City A to City B covering a distance of 240 km. It takes 4 hours to complete the trip.
- What is the average speed of the truck?
- If the truck continues at the same speed, how far will it travel in 7.5 hours?
Solution
1. Average Speed
Use ( s = \dfrac{d}{t} )
[ s = \frac{240\ \text{km}}{4\ \text{h}} = 60\ \text{km/h} ]
Answer: 60 km/h
2. Distance in 7.5 Hours
Use ( d = s \times t )
[ d = 60\ \text{km/h} \times 7.5\ \text{h} = 450\ \text{km} ]
Answer: 450 km
Check Dimensions
- Speed: km/h ✔️
- Time: hours ✔️
- Distance: km ✔️
4. Quick Revision Summary
| Concept | Formula | Example Result |
|---|---|---|
| Distance | (d = s \times t) | 240 km |
| Speed | (s = d/t) | 60 km/h |
| Time | (t = d/s) | 4 h |
| Units | Convert minutes → hours: (1\ \text{min} = \dfrac{1}{60}\ \text{h}) | 7.5 h = 450 km |
| Multi‑segment | Sum distances or times separately | – |
| Conversion | (1\ \text{km} = 1000\ \text{m}); (1\ \text{h} = 60\ \text{min}) | – |
Mnemonic
“Speed times Time gives Distance.”
(ST → D)
Quick Practice Questions
- A train travels 180 km in 3 hours. What is its speed?
- A cyclist covers 10 km in 30 minutes. How long will it take to cover 50 km at the same speed?
- A car travels 120 km at 60 km/h. How many minutes did it take?
(Try solving before checking the answer sheet.)
End of Notes
Good luck with your preparation! 🚀