TIME, SPEED AND DISTANCE

BASIC CONCEPTS

Distance
• Length covered by a moving object
• Usually measured in kilometres or metres

Time
• Duration taken to cover distance
• Measured in hours, minutes, or seconds

Speed
• Rate of change of distance with time

Basic Formula
• Speed = Distance / Time
• Distance = Speed × Time
• Time = Distance / Speed

UNITS AND CONVERSION (VERY IMPORTANT)

Common Conversions
• 1 km = 1000 m
• 1 hour = 60 minutes = 3600 seconds

Speed Conversion
• km/hr to m/s → multiply by 5/18
• m/s to km/hr → multiply by 18/5

CSAT Tip
• Always convert units first to avoid mistakes

AVERAGE SPEED (MOST IMPORTANT CONCEPT)

Definition
• Average speed = Total distance / Total time

Key Insight
• Average speed is NOT the average of speeds unless distances are equal

Example Logic
• Going and returning with same speed → average speed = same speed
• Equal distances at different speeds → use harmonic logic

Special Formula (Equal Distance)
• Average speed = (2ab) / (a + b)

ROUND TRIP PROBLEMS

Concept
• Total distance = onward distance + return distance
• Total time = time taken in both directions

CSAT Trap
• Do not take average of speeds directly

RELATIVE SPEED

Meaning
• Speed of one object with respect to another

Same Direction
• Relative speed = Difference of speeds

Opposite Direction
• Relative speed = Sum of speeds

Application
• Trains crossing each other
• Races
• Moving objects comparison

TRAIN PROBLEMS

Important Idea
• Length of train matters

Cases
• Train crossing a pole → distance = length of train
• Train crossing a platform → distance = length of train + length of platform
• Two trains crossing → sum of lengths

BOAT AND STREAM 

Terms
• Downstream speed = Boat speed + Stream speed
• Upstream speed = Boat speed − Stream speed

Key Insight
• Boat speed = (Downstream + Upstream) / 2
• Stream speed = (Downstream − Upstream) / 2

RACE PROBLEMS 

Concept
• Distance covered is same
• Faster runner gives a lead to slower one

CSAT Tip
• Convert race problems into ratio of speeds

TIME AND DISTANCE GRAPH 

• Straight line indicates uniform speed
• Steeper line indicates higher speed
• Flat line indicates rest

PRACTICE QUESTIONS 

Question 1
A person travels a distance of 60 km at a speed of 30 km/hr and returns at a speed of 20 km/hr. Find the average speed for the entire journey.

Question 2
Two trains of lengths 100 m and 150 m are running in opposite directions at speeds of 36 km/hr and 54 km/hr respectively. In how many seconds will they cross each other?

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Subject: CSAT

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