Speed measures how fast an object moves. Distance is the path covered. Time is the duration taken. These three are linked by a simple relationship that forms the base of all calculations
💡Key Formulas
• Speed = Distance/Time (S = D/T)
• Distance = Speed × Time (D = S × T)
• Time = Distance/Speed (T = D/S)
Unit Conversions (Critical for SSC):
• km/hr to m/s: Multiply by 5/18
• m/s to km/hr: Multiply by 18/5
• 1 km/hr = 5/18 m/s
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Exam Patterns
What examiners ask — read before attempting PYQs
⚡Shortcut 1 - Unit Conversion Trick
To convert km/hr to m/s, multiply by 5/18
💡Remember
36 km/hr = 10 m/s (this is a standard conversion to memorize)
Convert to m/s
Speed in m/s = 60 × 5/18 = 300/18 = 16.67 m/s
Answer: 16.67 m/s
Worked Example 2:
A train running at 54 km/hr takes 20 seconds to cross a platform 200m long. Find the length of the train.
1
Convert speed to m/s
54 km/hr = 54 × 5/18 = 15 m/s
2
Find total distance covered
Distance = Speed × Time = 15 × 20 = 300m
3
Find train length
Train length = Total distance - Platform length = 300 - 200 = 100m
Answer: 100 meters
Shortcut 3 - Relative Speed:
• Same direction: Relative speed = |S1 - S2|
• Opposite direction: Relative speed = S1 + S2
Most Common Trap (#1 Mistake):
Students forget unit conversions! SSC deliberately mixes km/hr and m/s in the same question. Always check units in options and convert accordingly. Questions asking for train crossing times usually need m/s, while car journey problems often use km/hr.
Another frequent error is confusing relative motion directions. When two objects move toward each other, add their speeds. When moving in the same direction, subtract speeds.
Time-based problems often trick students with percentage changes in speed
💡Remember
if speed increases by 25%, time decreases by 20% (not 25%). Use the reciprocal relationship carefully.
Practice identifying whether the question asks for train length, crossing time, or platform length. Each requires different approaches but uses the same core formula.
🔑 Key Points
Master formula: Speed = Distance/Time and its variations D = S × T and T = D/S
Unit conversion: km/hr to m/s multiply by 5/18, m/s to km/hr multiply by 18/5
Standard conversion: 36 km/hr = 10 m/s (memorize this)
Relative speed: same direction subtract speeds, opposite direction add speeds
Train problems: Total distance = Train length + Platform/Bridge length
Speed increase by x%: New time = Original time × 100/(100+x)
Speed decrease by x%: New time = Original time × 100/(100-x)
Always check units in answer options before solving
Average speed = Total distance/Total time (not average of individual speeds)
Time and speed are inversely proportional when distance is constant
📌 Exam Facts
1 km/hr equals exactly 5/18 m/s
36 km/hr equals exactly 10 m/s
72 km/hr equals exactly 20 m/s
Average speed formula: Total distance divided by total time
Relative speed when objects move toward each other: Sum of individual speeds
Relative speed when objects move in same direction: Difference of individual speeds
When speed increases by 20%, time decreases by 16.67%
When speed decreases by 20%, time increases by 25%
Questions Asked in Previous Exams
Real questions from SSC papers — 2015 to 2024 · Showing 3 of 6
Exam Q 12022Previous Year Pattern
Two runners start from the same point. Runner A runs at 8 m/s and Runner B runs at 6 m/s in the same direction. After how many seconds will Runner A be 100 metres ahead of Runner B?
Exam Q 22022Previous Year Pattern
A man walks 3 km in 45 minutes. If he walks at the same speed, how much distance will he cover in 2 hours 15 minutes?
Exam Q 32022Previous Year Pattern
A train travels from Station A to Station B, covering the first 120 km at 60 km/h and the next 180 km at 90 km/h. A car starts from Station A at the same time and travels at a constant speed. If the car reaches Station B exactly when the train does, what is the car's speed in km/h?
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3 more PYQ questions — free with an account
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