Time‑Speed‑Distance – Study Notes
Subject: Quantitative Aptitude – Manipur PSC
Topic: Time‑Speed‑Distance (TSD)
1. Simple Explanation
The Time‑Speed‑Distance relationship is a fundamental concept in physics and everyday life.
It tells us how the distance travelled by an object, the speed at which it moves, and the time it takes are inter‑dependent.
- Speed (v) – how fast an object moves (units: km/h, m/s, etc.)
- Distance (d) – how far the object travels (units: km, m, etc.)
- Time (t) – how long the travel lasts (units: h, s, etc.)
The basic formulae are:
| Formula | Meaning | Units |
|---|---|---|
| ( v = \frac{d}{t} ) | Speed = Distance ÷ Time | km/h or m/s |
| ( d = v \times t ) | Distance = Speed × Time | km or m |
| ( t = \frac{d}{v} ) | Time = Distance ÷ Speed | h or s |
These equations hold as long as the speed is constant (uniform motion).
2. Key Points & Concepts
| Concept | What to Remember | Typical Exam Hint |
|---|---|---|
| Units | Keep all quantities in the same system (e.g., km & h). Convert if necessary. | If distance is in km and speed in km/h, time will be in hours. |
| Speed vs. Velocity | Only speed (magnitude) is used in TSD problems; direction is ignored unless “relative speed” is specified. | Look for words like “towards”, “away from” → relative speed. |
| Relative Speed | When two objects move towards/away from each other, their speeds add/subtract. | “Two trains start from A and B towards each other” → use (v_1 + v_2). |
| Time to Cover a Distance | Use (t = d/v). If the speed is given as average speed, use the same formula. | If the problem says “average speed”, ignore any acceleration/deceleration. |
| Changing Speed | If speed changes, split the journey into segments, compute each distance/time separately, then add. | “A car travels 60 km/h for 2 h and then 80 km/h for 1 h.” |
| Distance covered in a Time | (d = v \times t). | Useful when you know how long an object has been moving. |
| Speed from Distance & Time | (v = d/t). | Often used in “find the speed” questions. |
| Ratio problems | Express distances or times as ratios; convert to actual values using the formulas. | “If one train is twice as fast as another, how long will it take to cover the same distance?” |
| Decoding the Question | Identify what is asked: distance, speed, or time. | Look for keywords: “how long”, “how fast”, “how far”. |
3. Worked Example
Problem (Manipur PSC style)
Two cars start simultaneously from towns A and B which are 240 km apart. Car‑A moves towards B at 80 km/h, while Car‑B moves towards A at 60 km/h. They meet after how many hours?
Step‑by‑Step Solution
-
Identify the required quantity:
We need the time until the cars meet. -
Determine the relative speed:
Since they move toward each other, add their speeds.
[ v_{\text{rel}} = 80 + 60 = 140 \text{ km/h} ] -
Use the Distance–Speed–Time relation for the whole distance (240 km):
[ t = \frac{d}{v_{\text{rel}}} = \frac{240}{140} ] -
Simplify the fraction:
[ t = \frac{240}{140} = \frac{12}{7} \text{ h} \approx 1.714 \text{ h} ] -
Convert to hours and minutes (optional):
[ 0.714 \text{ h} \times 60 \approx 42.8 \text{ min} ] So, they meet after about 1 hour 43 minutes.
Quick Check
- Car‑A travels (80 \times 1.714 \approx 137) km.
- Car‑B travels (60 \times 1.714 \approx 103) km.
- Sum ≈ 240 km → correct.
4. Quick Revision Summary
-
Core Equations
- (v = d/t)
- (d = v \times t)
- (t = d/v)
-
Relative Speed
- Toward each other: add speeds.
- Away from each other: subtract slower speed from faster speed.
-
Unit Consistency
- If distance in km & speed in km/h → time in hours.
- Convert to minutes if required: ( \text{minutes} = \text{hours} \times 60).
-
Breaking Down Journeys
- For changing speeds, treat each segment separately:
[ d_{\text{total}} = \sum v_i \
- For changing speeds, treat each segment separately: