This document provides an overview of concepts related to time, speed, and distance (TSD). It begins with the basics of TSD relationships, including how distance, time, and speed are directly or inversely proportional. It then provides examples of average speed calculations and problems involving distance, speed, and time. Next, it covers relative speed and examples of problems involving objects moving in the same or opposite directions. Finally, it discusses to-and-fro motion in a straight line, providing examples of objects moving in both the same and opposite directions between two points. The document aims to explain key TSD concepts and relationships through examples and practice problems.

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Time, Speed and Distance
Concept Session 1

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Chapter Pathway
TSD Basics
Average
speed
Relative
speed
To and fro
motion in a
straight Line
Circular
Motion
Trains
Boats and
Streams
Races
Miscellaneous

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TSD Basics

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Constant Time Speed Distance
Relationship
between the other
two variables
D varies directly
with S
𝐷 ∝ 𝑆
𝐷1
𝐷2
=
𝑆1
𝑆2
D varies directly
with T
𝐷 ∝ 𝑇
𝐷1
𝐷2
=
𝑇1
𝑇2
T varies Inversely
with S
𝑇 ∝
1
𝑆
𝑇1
𝑇2
=
𝑆2
𝑆1
TSD - Basics

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Average Speed

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Priya rides her motorcyle along the four sides 𝑎, 𝑏, 𝑐 and 𝑑 of a square field at speeds
of 20kmph, 40kmph, 60kmph and 80kmph respectively. Find the average speed of the
motorcycle around the field.
1. 42.4kmph
2. 38.4kmph
3. 48kmph
4. none of these
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑠𝑝𝑒𝑒𝑑 =
𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑡𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒
Average Speed
Answer: Option 2

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A train can complete a journey in 10 hours. It travels first half of the distance of
the journey at the rate 21 kmph and second half at the rate of 24 kmph. Find
the total distance travelled by the train in the journey. (in km)
1. 220
2. 224
3. 235
4. 242
Problems on D,S and T
Answer: Option 2

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Arun covered half the distance from his office to home at a speed of 7kmph and
for exactly half of the remaining time he travelled at 15kmph and the remaining
time at 20kmph. Find his average speed. ( in kmph)
1. 12
2. 10
3. 15
4. 9
Problems on D,S and T
Answer: Option 2

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A train approaches a tunnel AB. Inside the tunnel is a cat located at a point that
is
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8
𝑡ℎ of the distance AB measured from the entrance A. When the train
whistles the cat runs. If the cat moves to the entrance of the tunnel, A, the train
catches the cat exactly at the entrance. If the cat moves to the exit, B, the train
catches the cat at exactly the exit. The speed of the train is greater than the
speed of the cat by what order?
1. 3:1
2. 4:1
3. 5:1
4. None of these
Problems on D,S and T
Answer: option 1
CAT 2002

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Distance = 810kms. When speed is increased by 3km/hr time is decreased by
9hrs. what is the original speed? (in km/hr)
1) 15
2) 18
3) 20
4) 21
Given: d, Δs, Δt
To find: rest
Problems on D,S and T
Answer: Option 1

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When A increases his speed from 40km/hr to 50km/hr his time for the journey
decreases by 4 hrs. How long does it take for him to complete his journey @
40km/hr?
1. 18
2. 20
3. 21
4. 24
Given: Δs, Δt and Si/Sf or Ti/Tf
To Find : rest
Problems on D,S and T
Answer: Option 2

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A train met with an accident 180 km from station A. It completed the remaining
journey at 5/6th of its previous speed and reached two hours late at station B.
Had the accident taken place 400km further, it would have been only 1 hour
late.
1. What is the speed of the train?
2. What is the distance between A and B?
Problems on D,S and T
Answer: 1. 80 km/hr
2. 980 Km

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For a given distance when speed is decreased by 10km/hr, the duration of the
journey increases by 40 hours. If the speed is increased by 5km/hr from the
original speed, the duration of the journey is decreased by 10 hours. Find the
distance covered. (in km)
1. 1800
2. 2000
3. 1500
4. 2450
Problems on D,S and T
Answer: Option 3
Given: two Δs and corresponding Δt or vice versa

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Relative Speed

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Relative speed
When in same direction,
𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑆𝑝𝑒𝑒𝑑 = 𝑆𝑝𝑒𝑒𝑑 𝑓𝑎𝑠𝑡𝑒𝑟 − 𝑆𝑝𝑒𝑒𝑑 𝑆𝑙𝑜𝑤𝑒𝑟
When in opposite direction,
𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑆𝑝𝑒𝑒𝑑 = 𝑆𝑝𝑒𝑒𝑑 𝑓𝑎𝑠𝑡𝑒𝑟 + 𝑆𝑝𝑒𝑒𝑑 𝑆𝑙𝑜𝑤𝑒𝑟

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A thief committed a burglary and started fleeing at 12noon at a speed of
60km/hr. he was then chased by a policeman X. X started the chase, 15 min
after the thief had started, at a speed of 65kmph.
At what time did X catch the thief?
1. 3:00pm
2. 3.15pm
3. 3:30pm
4. 3:28pm
Problems on Relative speed
Answer: option 2
CAT 1997

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A,B and C start from the same place and travel in the same direction at speeds
of 30, 40 and 60km/hr respectively. B starts two hours after A. if B and C
overtake A at the same instant, how many hours after A did C start?
1. 4hrs
2. 3hrs
3. 3.6hrs
4. 4.2hrs
Problems on Relative speed
Answer: option 1
CAT 2006

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To and Fro Motion in a Straight Line

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Opposite directions
Distance between P and Q is 900m. If speed of A is 50m/sec and speed of B is 40 m/sec.
A @ P and B @ Q
1. How far will they travel before they are together for the 1st time, 2nd time and nth
time?
2. How long will they take before they are together for the 1st , 2nd time and nth
time?
3. How far from P will they be together for the 1st time, 2nd time and nth time?
4. Will they ever be together at P or Q? If so after how long will they meet for the
first time @ P or Q?
5. If they are together for the 7th time at S. what is the distance between S and Q?
6. What is the ratio of time taken by A and B respectively to reach Q and P
respectively for the first time?
7. What is the ratio of time taken by A and B respectively by A and b to reach Q and
P respectively after meeting each other for the first time at M between P and Q?
To and fro motion in a straight line

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Same directions
Distance between P and Q is 900m. If speed of A is 50m/sec and speed of B is 40 m/sec.
A and B are at P in the start.
1. How far will they travel before they meet for the 1st time, 2nd time and nth time?
2. How long will they take before they are together for the 1st , 2nd time and nth
time?
3. How far from P will they meet for the 1st time, 2nd time and nth time?
4. Will they ever meet at P or Q? If so after how long will they meet for the first time
@ P or Q?
5. If they meet for the 7th time at S. what is the distance between S and Q?
6. At how many distinct points will they meet including P and Q?
To and fro motion in a straight line