Describing Motion Around Us (Class 9): Notes और MCQ Practice

आसान भाषा में:

जब कोई object समय के साथ किसी fixed reference point के respect में अपनी position बदलता है, तो वह motion में होता है। Straight line motion सबसे simple motion है। इसमें हम यह मापते हैं कि कोई चीज कितनी दूर गई (distance), अपनी शुरुआत से असल में कितनी हटी (displacement), कितनी तेजी से चली (speed/velocity), और उसकी रफ्तार कितनी तेजी से बदली (acceleration)।

Key Points & Formulas:

• Reference Point (Origin 'O'): किसी object की position बताने के लिए चुना गया fixed point।
• Distance vs Displacement:
• Distance: कुल तय किया गया path length (दिशा की जरूरत नहीं)।
• Displacement: Initial और final position के बीच का net change (magnitude + direction दोनों जरूरी)। SI unit: metre (m).
• Displacement का magnitude हमेशा distance से कम या उसके बराबर होता है (Displacement ≤ Distance)।
• Average Speed: Total distance travelled ÷ Time interval (SI unit: m s⁻¹ या m/s).
• Average Velocity (vav): Displacement ÷ Time interval = s ÷ t (SI unit: m s⁻¹).
• Average Acceleration (a): Rate of change of velocity = (v − u) ÷ (t₂ − t₁). SI unit: m s⁻².
• Speeding up: Acceleration velocity की दिशा में होता है।
• Slowing down: Acceleration velocity की उल्टी दिशा में होता है (negative sign).
• Earth की gravity में नीचे गिरती वस्तु का acceleration constant होता है: g = 9.8 m s⁻².

Memory Tricks:

1. "Displacement = Direct Short-cut": Distance पूरा चक्कर है, पर Displacement सिर्फ initial से final point तक का 'direct' फासला है।
2. "Brake माने Minus": Accelerator दबाओगे तो a और v 'साथ-साथ' (same direction, positive); Brake दबाओगे तो a 'उलटा' (opposite direction, negative)!

Common Board-Exam Mistakes:

1. Distance और Displacement को एक समझना: अगर कोई जाकर वापस उसी point पर आ जाए, तो Displacement = 0 m होता है, लेकिन Distance zero नहीं होता!
2. Units convert न करना: Speed अगर km h⁻¹ में दी हो और time seconds में, तो पहले km h⁻¹ को m s⁻¹ में बदलें (1 km h⁻¹ = 1000 m ÷ 3600 s)!

Describing Motion Around Us

1. Chapter in Short

This chapter introduces the fundamental concepts needed to describe motion in our everyday world. Motion is the change in the position of an object over time with respect to a fixed reference point. The chapter focuses on the simplest type of motion—linear motion (motion in a straight line). It explains the clear differences between distance and displacement, speed and velocity, and introduces the concept of acceleration (how fast velocity changes). It also shows how motion can be represented using numbers, formulas, and graphs.

2. Key Concepts Explained Simply

A. Reference Point and Position

• To say whether an object is moving or where it is located, we always need a fixed starting point called the reference point (or origin 'O').
• The position of an object is described by both its distance from the reference point and its direction.
• Motion vs. Rest: If an object's position changes with time relative to the reference point, it is in motion. If its position does not change, it is at rest.
• Everyday Example: An athlete running on a straight track starting from a line marked '0 m'. The starting line is the reference point. Points to the right are taken as positive (+), and points to the left as negative (−).

B. Instant of Time vs. Time Interval

• An instant of time is a single clock reading at a specific moment (e.g., at 10 seconds).
• A time interval is the duration between two clock readings (e.g., from 4 seconds to 10 seconds, the interval is 10 − 4 = 6 seconds).

C. Distance Travelled vs. Displacement

• Distance travelled: The actual total path length covered by an object during its motion. It needs only a numerical value (magnitude) and unit, not direction.
• Displacement: The net change in position of an object between two instants of time (the shortest straight-line distance from the initial position to the final position, along with direction).
• Everyday Example: If an athlete runs 100 m forward from point O to point A, and then runs 60 m back to point B (which is 40 m from O):
• Total distance travelled = 100 m + 60 m = 160 m
• Displacement = 40 m in the positive direction (from O to B).
• Important Rule: Total distance and the magnitude of displacement are equal only if an object moves in a straight line in one direction without turning back.

D. Average Speed and Average Velocity

• Average Speed: Tells how fast an object moves regardless of direction. It is the total distance covered divided by the time taken.
• Average Velocity: Tells how fast the position of an object changes and in which direction. It is the displacement divided by the time interval.
• Everyday Example: If a swimmer swims 25 m to the other end of a pool and returns 25 m back to the starting point in 50 s:
• Total distance = 50 m → Average speed = 50 m ÷ 50 s = 1 m/s
• Displacement = 0 m → Average velocity = 0 m ÷ 50 s = 0 m/s

E. Uniform and Non-Uniform Motion

• Uniform motion in a straight line: An object covers equal distances in equal intervals of time (moves at a constant speed).
• Non-uniform motion in a straight line: An object covers unequal distances in equal intervals of time (moves with increasing or decreasing speed).

F. Average Acceleration

• Acceleration measures how quickly the velocity of an object changes.
• If an object speeds up, the acceleration is in the direction of velocity.
• If an object slows down (like when brakes are applied), the acceleration is opposite to the direction of velocity (represented with a minus sign).
• Key Fact: An object moving at a constant high velocity has zero acceleration because its velocity is not changing at all.

3. Important Definitions, Formulas, Facts, and Dates

Definitions

• Linear Motion: Motion of an object in a straight line.
• Reference Point: A fixed point used to describe the location and motion of an object.
• Displacement: The net change in the position of an object between two given instants of time.
• Average Speed: The total distance travelled divided by the time interval.
• Average Velocity: The displacement (change in position) divided by the time interval.
• Average Acceleration: The change in velocity divided by the time interval.
• Rate of Change: The ratio of change in one physical quantity to the corresponding change in time.

Important Formulas

• Average Speed:

Average speed = Total distance travelled ÷ Time interval

• Average Velocity:

vav = Displacement ÷ Time interval = s ÷ t

• Average Acceleration:

a = (Final velocity − Initial velocity) ÷ Time interval = (v − u) ÷ (t2 − t1)

• Unit Conversion:

1 km/h = 1000 m ÷ 3600 s = 5 ÷ 18 m/s

Units

• Distance and Displacement: Metre (m)
• Speed and Velocity: Metre per second (m s⁻¹ or m/s); also measured in km h⁻¹
• Acceleration: Metre per second squared (m s⁻² or m/s²)

Historical Facts

• The concept of speed as distance divided by time is found in ancient Indian treatises, including the Aryabhatiya (5th century CE) and the mathematical text Ganitakaumudi (14th century CE).
• Acceleration of an object falling freely under Earth's gravity near the surface is constant and denoted by g = 9.8 m s⁻².

4. Solved Examples (Board-Exam Style)

Example 1 (Ancient Indian Problem - Ganitakaumudi)

Question: Two postmen start walking towards each other from a distance of 210 yojanas. One travels 9 yojanas per day and the other covers 5 yojanas per day. In how many days will they meet each other?

Answer:

• Combined distance covered by both postmen in one day = 9 yojanas + 5 yojanas = 14 yojanas.
• Total distance to be covered = 210 yojanas.
• Time taken = Total distance ÷ Combined speed per day
• Time = 210 ÷ 14 = 15 days.
• Therefore, they will meet each other after 15 days.

Example 2 (Average Speed vs. Average Velocity)

Question: A family drives 200 km north in 3 hours. Afterwards, they drive 200 km south back to their starting position in 2 hours. Calculate their average speed and average velocity for the entire trip.

Answer:

• Total distance travelled = 200 km + 200 km = 400 km
• Total time taken = 3 h + 2 h = 5 h
• Average speed = Total distance ÷ Total time = 400 km ÷ 5 h = 80 km/h
• Since they returned to the starting position, net displacement = 0 km
• Average velocity = Displacement ÷ Total time = 0 km ÷ 5 h = 0 km/h

Example 3 (Acceleration and Deceleration)

Question: A bus is travelling along a straight highway at 36 km/h. The driver accelerates for 10 s, increasing the velocity to 54 km/h. Later, the driver applies brakes and the bus stops in 5 s. Find the average acceleration in both situations.

Answer:

• Part (i): When accelerating
• Initial velocity (u) = 36 km/h = 36 × (1000 ÷ 3600) = 10 m/s
• Final velocity (v) = 54 km/h = 54 × (1000 ÷ 3600) = 15 m/s
• Time (t) = 10 s
• a = (v − u) ÷ t = (15 − 10) ÷ 10 = 5 ÷ 10 = 0.5 m s⁻² (in the direction of velocity)
• Part (ii): When brakes are applied
• Initial velocity (u) = 15 m/s
• Final velocity (v) = 0 m/s (bus comes to a stop)
• Time (t) = 5 s
• a = (v − u) ÷ t = (0 − 15) ÷ 5 = −15 ÷ 5 = −3 m s⁻²
• The negative sign shows that acceleration acts opposite to the direction of motion.

Example 4 (Free Fall Acceleration)

Question: An object is dropped from rest from a height. Its velocity after 1 s is 9.8 m/s, after 2 s is 19.6 m/s, and after 3 s is 29.4 m/s. Calculate the acceleration between 1 s and 2 s, and between 2 s and 3 s. Is it constant?

Answer:

• Acceleration between 1 s and 2 s:

a = (19.6 − 9.8) ÷ (2 − 1) = 9.8 ÷ 1 = 9.8 m s⁻²

• Acceleration between 2 s and 3 s:

a = (29.4 − 19.6) ÷ (3 − 2) = 9.8 ÷ 1 = 9.8 m s⁻²

• Yes, the acceleration is constant and equals 9.8 m s⁻², directed vertically downward (acceleration due to gravity, g).

5. Common Mistakes and Quick Revision Points

• Mistake: Confusing distance with displacement.
• Correction: Distance is always positive and cannot decrease as an object moves. Displacement can be positive, negative, or zero.
• Mistake: Thinking high speed means high acceleration.
• Correction: Acceleration depends only on the rate of change of velocity. A train moving at a constant speed of 120 km/h on a straight track has zero acceleration.
• Mistake: Forgetting to convert units to SI units.
• Correction: If speed is given in km/h and time in seconds, convert km/h to m/s by multiplying by (1000 ÷ 3600) before using acceleration formulas.
• Displacement Magnitude vs. Distance: Magnitude of displacement is always less than or equal to the total distance travelled (it is never greater).
• When are they equal? Distance = magnitude of displacement, and average speed = magnitude of average velocity only when an object moves along a straight line in a single direction without reversing.