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Speed Distance Time

BSF Constable · Quantitative Aptitude

Also prepare for:CRPF Const CISF Const ITBP Const UP Const

Relative Speed →

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Core Concept

Read this first — the foundation of the topic

→Core Concept

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)

⚡Shortcut 2 - Distance Formula Rearrangement

1

Find speed in km/hr Speed = Distance/Time = 180/3 = 60 km/hr

2

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%

🚀 60-Second Revision

Formula: Speed = Distance/Time, Distance = Speed × Time, Time = Distance/Speed
Remember: 36 km/hr = 10 m/s for quick conversions
Unit conversion: km/hr to m/s multiply by 5/18
Trap: Always check if answer needs km/hr or m/s units
Relative speed: Add for opposite directions, subtract for same direction
Train crossing: Distance = Train length + Platform length
Speed-time relationship: Inversely proportional when distance is constant

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