Time, Speed & Distance
1. What is Time, Speed & Distance?
Time, Speed, and Distance are three related concepts used to measure how fast an object moves, how far it travels, and how long it takes. They are connected by a simple formula:
Speed = Distance / Time
Speed – How fast something moves
Distance – How far it moves
Time – How long it takes to move that distance
Examples:
| Quantity | Meaning | Example |
|---|---|---|
| Distance | Total path covered | 120 km |
| Speed | Rate of movement | 60 km/hr |
| Time | Duration of travel | 2 hours |
2. Basic Formulas
| Formula | Description | Example |
|---|---|---|
| Speed = Distance / Time | To find speed | 120 ÷ 2 = 60 km/hr |
| Distance = Speed × Time | To find distance | 60 × 2 = 120 km |
| Time = Distance / Speed | To find time | 120 ÷ 60 = 2 hr |
3. Conversion Units
| Conversion | Formula |
|---|---|
| 1 km/hr = 5/18 m/s | Multiply km/hr by 5/18 to get m/s |
| 1 m/s = 18/5 km/hr | Multiply m/s by 18/5 to get km/hr |
| 1 hour = 60 minutes = 3600 seconds | Time unit conversions |
Example:
Convert 72 km/hr to m/s
72 × 5/18 = 20 m/s
4. Average Speed
If the distance is same but speeds are different:
Average Speed = 2xy / (x + y)
where x and y are the two speeds
Example:
A car travels to a city at 60 km/hr and returns at 40 km/hr.
Average Speed = (2 × 60 × 40) / (60 + 40) = 48 km/hr
5. Relative Speed
When two bodies move towards or away from each other:
| Situation | Formula |
|---|---|
| Moving in same direction | Relative Speed = (A – B) |
| Moving in opposite direction | Relative Speed = (A + B) |
Example:
Two trains move in opposite directions at 40 km/hr and 60 km/hr.
Relative Speed = 40 + 60 = 100 km/hr
6. Key Concepts & Short Tricks
| Concept | Formula / Trick | Example |
|---|---|---|
| If distance is constant | Speed ∝ 1/Time | More speed → Less time |
| If time is constant | Distance ∝ Speed | Double speed → Double distance |
| If speed is constant | Distance ∝ Time | Double time → Double distance |
| When two objects meet | (A's Distance / B's Distance) = (A's Speed / B's Speed) | Used in meeting problems |
7. Train Problems (Important for Exams)
| Type | Formula / Approach |
|---|---|
| Train crosses a stationary object | Time = Length / Speed |
| Train crosses a platform | Time = (Length of Train + Platform) / Speed |
| Two trains cross each other | Time = (Sum of Lengths) / Relative Speed |
Example:
A 200m train crosses a pole in 20s.
Speed = 200 / 20 = 10 m/s = 36 km/hr
8. Boat & Stream Problems
| Type | Formula |
|---|---|
| Speed in Still Water | (Downstream + Upstream) / 2 |
| Speed of Stream | (Downstream – Upstream) / 2 |
Example:
Downstream = 12 km/hr, Upstream = 8 km/hr
Speed in Still Water = (12 + 8)/2 = 10 km/hr
9. Important Short Notes
| Concept | Key Point |
|---|---|
| Speed increases | Time decreases |
| When distance is same | Ratio of speeds = inverse ratio of times |
| Unit consistency | Always use same units (km–hr or m–s) |
| Conversion | 1 km/hr = 5/18 m/s, 18 km/hr = 5 m/s |
10. Real-Life Analogy
Imagine you are driving a car:
Speed
How fast the car is moving
Time
How long you drive
Distance
How far you reach
If you increase speed, you reach faster (less time). If you drive longer, you cover more distance.
11. Common Delhi Police / SSC Exam Facts
Formula: Speed = Distance / Time
1 km/hr = 5/18 m/s
Average Speed for same distance = (2xy)/(x + y)
Relative Speed for opposite direction = Sum of speeds
Train crosses platform → add lengths
Downstream > Upstream
12. Quick Recap
| Concept | Summary |
|---|---|
| Speed | Distance covered per unit time |
| Distance | Product of speed and time |
| Time | Distance ÷ Speed |
| Relative Speed | Difference or sum depending on direction |
| Average Speed | (2xy)/(x + y) for equal distances |
| Boat & Stream | (Down ± Up)/2 formulas |
| Unit Conversion | 1 km/hr = 5/18 m/s |
You've completed Time, Speed & Distance Concepts!
Courage Tip: Remember the key formulas for time, speed, and distance calculations. Practice unit conversions and relative speed problems which are frequently asked in Delhi Police exams.
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