Lesson 4 � Intermediate

Time, Speed & Distance

TSD har exam mein aata hai. Trains, boats, relative speed � sab ispe based hai. Formulas simple hain but application tricky hoti hai. Chalo step by step seekhte hain.

? 28 min✓ Intermediate✓ Percentages

Basic formula

WHAT

Three interconnected quantities: Speed = Distance/Time, Distance = Speed � Time, Time = Distance/Speed. In teen mein se koi bhi do pata ho toh teesra nikal jaata hai.

WHEN

Trains crossing poles/platforms, boats in rivers, relative motion, average speed � sab mein ye formula use hota hai. MNC exams mein 3-5 questions aate hain.

WHERE

Unit conversion sabse important hai. km/hr se m/s: multiply by 5/18. m/s se km/hr: multiply by 18/5. Ye galat hua toh answer galat aayega.

Unit Conversion: km/hr ✓ m/s: � 5/18. m/s ✓ km/hr: � 18/5. Ye dooshra sabse common mistake hai exam mein. Yaad rakhlo: "18" bade number se chhote mein jaata hai.

Unit conversion table

# Important conversions:
# 1 km/hr = 5/18 m/s
# 1 m/s = 18/5 km/hr = 3.6 km/hr

# Speed ratios when time same:
# Speed ✓ Distance (same time mein)
# Agar A ne 100m 10 sec mein kiya, B ne 200m 10 sec mein
# A:B speed = 100:200 = 1:2

# Distance ratios when speed same:
# Distance ✓ Time (same speed pe)
# Agar A ne 2 ghante mein 100km kiya
# A ne 4 ghante mein 200km karega

# Average speed (multiple segments):
# Average speed = Total Distance / Total Time
# IMPORTANT: (s1 + s2)/2 galat hai jab distances same nahi hain
# Correct: 2�s1�s2/(s1+s2) jab distances same hon
# Correct: 3�s1�s2�s3/(s1�s2 + s2�s3 + s1�s3) jab teen hon

Train problems

Train problems mein do cheezein important hain � train ki length aur platform/pole ki length. Dono ko add karna padta hai:

# Train crossing a pole:
# Time = Train length / Speed
# (pole ki length 0 maani jaati hai)

# Train crossing a platform:
# Time = (Train length + Platform length) / Speed

# Two trains same direction:
# Relative speed = |S1 - S2|
# Time to cross = (L1 + L2) / (S1 - S2)

# Two trains opposite direction:
# Relative speed = S1 + S2
# Time to cross = (L1 + L2) / (S1 + S2)

# Example: 150m train, 200m platform, 54 km/hr
# Speed in m/s = 54 � 5/18 = 15 m/s
# Time = (150 + 200) / 15 = 350/15 = 23.33 sec

Boats & Streams

Nadi mein boat chalti hai � stream ki speed effect karti hai. Upstream (against flow) aur downstream (with flow) alag hote hain:

# Downstream (nadi ke saath):
# Speed = Boat speed + Stream speed = b + s

# Upstream (nadi ke khilaf):
# Speed = Boat speed - Stream speed = b - s

# Boat speed in still water:
# b = (Downstream + Upstream) / 2

# Stream speed:
# s = (Downstream - Upstream) / 2

# Example: Boat 10 km/hr chalti hai, stream 2 km/hr
# Downstream = 10 + 2 = 12 km/hr
# Upstream = 10 - 2 = 8 km/hr
# Time for 24km downstream = 24/12 = 2 hours

Relative Speed

Jab do objects move karein � same ya opposite direction mein � relative speed important hai:

# Same direction:
# Relative speed = |S1 - S2|

# Opposite direction:
# Relative speed = S1 + S2

# Circular track:
# Same direction: Time to meet = Track length / (S1 - S2)
# Opposite direction: Time to meet = Track length / (S1 + S2)

# Example: Two runners on 400m track
# A: 10 m/s, B: 8 m/s, same direction
# Time to meet = 400 / (10-8) = 200 seconds

# Example: Opposite direction
# Time to meet = 400 / (10+8) = 22.22 seconds

Shortcut: Circular track problems mein same direction mein time zyada lagta hai (chhoti relative speed), opposite direction mein kam (badi relative speed). Jaldi guess kar sakte ho answer.

Exercise

Question: 200m ki train 72 km/hr ki speed se ek pole ko cross karti hai. Time kitna lagega seconds mein? (Sirf number)

Question: Ek aadmi 10 km/hr se chalta hai. 2 ghante mein kitna distance cover karega km mein? (Sirf number)

Question: Boat ki speed still water mein 10 km/hr hai aur stream ki speed 2 km/hr hai. Downstream speed kitni hai km/hr mein? (Sirf number)

Question: 400m circular track pe do runners hain. A 10 m/s, B 8 m/s � same direction mein kitne seconds mein milenge? (Sirf number)

Common mistakes

Unit conversion bhool jaana: 72 km/hr = 72 � 5/18 = 20 m/s. Ye convert karna mat bhoolo.
Average speed galat nikalna: (s1+s2)/2 sirf tab sahi hai jab times same hon. Warna total distance / total time use karo.
Train problems mein length add karna bhoolna: Platform pe train cross karte hain toh dono lengths add karo.
Relative direction confuse karna: Same direction = subtract, opposite = add. Yaad rakhlo.

Lesson complete?

TSD samajh aa gaya✓ Ab Time & Work seekhte hain � ye pipes, cisterns aur work problems ke liye zaroori hai.