🚗 Time Speed Distance - Formula Sheet

🎯 Basic Formulas

Speed, Time, Distance

Speed = Distance / Time
Time = Distance / Speed
Distance = Speed × Time

Unit Conversions

km/hr to m/s: Multiply by 5/18
m/s to km/hr: Multiply by 18/5

📊 Relative Speed

Same Direction

Relative Speed = |Speed₁ - Speed₂|

Opposite Direction

Relative Speed = Speed₁ + Speed₂

Time to Meet/Catch

Time = Distance / Relative Speed

🔢 Special Cases

Train Problems

Time to pass pole = Length / Speed
Time to pass platform = (Train + Platform) / Speed
Time to pass another train = (Train₁ + Train₂) / Relative Speed

Boat and Stream

Downstream Speed = Boat Speed + Stream Speed
Upstream Speed = Boat Speed - Stream Speed
Boat Speed = (Downstream + Upstream) / 2
Stream Speed = (Downstream - Upstream) / 2

Average Speed

Average Speed = Total Distance / Total Time
For equal distances: 2ab/(a + b)
For equal times: (a + b)/2

⚡ Quick Calculations

Journey Problems

If speed changes mid-journey:
Total Time = Time₁ + Time₂
Total Distance = Distance₁ + Distance₂

Head Start

Time to catch = Head Start / Relative Speed

Races

Winner's advantage = Time × Speed difference
Head start needed = Time × Speed difference

📝 Problem Types

Direct Problems

1. Find time/distance/speed using basic formula
2. Unit conversion problems
3. Average speed calculations

Relative Motion

1. Two objects moving towards/away from each other
2. Catch up problems with head start
3. Train crossing problems

Practical Applications

1. Boat and stream problems
2. Race track problems
3. Journey with breaks problems

🔍 Important Notes

1. Always check units before calculating
2. Relative speed depends on direction
3. Average speed ≠ (sum of speeds)/2
4. For trains, add lengths when crossing
5. Convert units consistently

Master TSD - Units and relative speed are crucial! 🚗