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Class 9 Science · Chapter 4 · Part 1 of 2
Describing Motion Around Us
Position, Distance, Displacement, Average Speed, Average Velocity, Average Acceleration
📍 Position
📏 Distance & Displacement
⚡ Speed & Velocity
🚀 Acceleration
PART 1
This part covers: Motion in a Straight Line → Position → Distance & Displacement → Average Speed & Velocity → Average Acceleration. Part 2 covers Graphs, Kinematic Equations & Circular Motion.
📌 Jump to Section
Motion in Straight Line
Position
Distance & Displacement
Speed & Velocity
Acceleration
Definitions
Exam FAQs
🌍 Introduction — Motion in Nature
Everything in nature is in motion — from massive astronomical objects to subatomic particles. Butterflies flitting, snakes slithering, horses galloping, ocean tides rising and falling — motion is everywhere!
To study complex motion, scientists first study idealised simplified forms: linear, circular, and oscillatory motion. In this chapter, we focus on linear motion (straight line) and uniform circular motion.
4.1 Motion in a Straight Line
📖 Definition
Linear motion (motion in a straight line) — When an object moves in a straight line, its motion is called linear motion. It is the simplest kind of motion. Examples: swimming race, falling ball, car on a straight highway, train on a straight track.
📍 4.1.1 Describing Position
To describe an object’s position, we need a fixed point called the reference point (origin).
- The distance and direction of the object from the reference point, at any instant, describes its position.
- If position changes with time → object is in motion.
- If position does not change with time → object is at rest.
- For straight line motion, direction is shown using plus (+) and minus (−) signs. Right of reference point = positive; left = negative.
💡 Note — Instant vs Time Interval
An instant of time is a single reading of a clock at a given point of time. A time interval is the time duration between two instants of time (between two clock readings).
📏 4.1.2 Distance Travelled and Displacement
An athlete starts at O (t=0s), reaches B (t=4s), reaches A (t=10s), then runs back to B (t=16s).
- Total distance travelled = OA + AB = 100 m + 60 m = 160 m
- Distance between start and stop positions = OB = 40 m (different from total distance!)
📖 Definition — Displacement
Displacement — The net change in the position of an object between two given instants of time. Requires both magnitude (numerical value with units) and direction.
- Magnitude of displacement = distance between object’s positions at the two instants
- Direction = from position at first instant towards position at second instant
- SI unit of both distance and displacement = metre (m)
🎯 Exam Point
Between t=0s and t=16s: Total distance = 160 m, but Displacement = 40 m (positive direction). These two are NOT equal when object turns back!
💡 Important Rule
For motion in a straight line, total distance travelled = magnitude of displacement ONLY IF the object moves without turning back (i.e., moves in one direction only). If it turns back, distance > displacement.
🧪 Activity 4.1 — Ball Thrown Vertically Upward
Setup: A ball is thrown vertically upward from O. It moves up to B then falls back to O. (Even though shown on two lines for clarity, it’s actually the SAME straight line motion.)
| Position | Total Distance from O | Displacement from O |
|---|---|---|
| O (start) | 0 cm | 0 cm |
| A | 40 cm | 40 cm (upward) |
| B (highest) | 140 cm | 140 cm (upward) |
| C (coming down) | 200 cm | 80 cm (upward) |
| O (back to start) | 280 cm | 0 cm |
Conclusion: Displacement’s magnitude is less than or equal to the total distance travelled — never greater.
✅ Check Your Understanding — Distance & Displacement
Q1. The SI unit of both distance and displacement is:
AKilometre
BMetre
CMetre per second
DSecond
Q2. Displacement is equal to distance travelled when an object:
AMoves in a circle
BMoves in one direction without turning back
CAlways (in every case)
DComes back to starting point
Q3. A complete description of displacement requires:
AOnly magnitude
BOnly direction
CBoth magnitude and direction
DOnly time taken
📋 Answer Key
Q1B — Metre. Both distance and displacement share the SI unit metre (m).
Q2B — Moves without turning back. If the object doesn’t reverse direction, total distance equals displacement magnitude.
Q3C — Both magnitude and direction. Displacement is a vector quantity requiring both components for complete description.
⚡ 4.1.3 Average Speed and Average Velocity
📖 Definition — Average Speed
Average speed — Total distance travelled divided by the time interval. Has no direction, only numerical value.
Eq. 4.1
Average Speed = Total Distance Travelled ÷ Time Interval
Uniform vs Non-Uniform Motion
| Type | Description |
|---|---|
| Uniform Motion | Object travels equal distances in equal intervals of time (for all time intervals). Speed is constant. |
| Non-Uniform Motion | Object travels unequal distances in equal intervals of time. Speed is increasing, decreasing, or both. |
🇮🇳 India’s Scientific Contributions
The concept of speed = distance ÷ time dates back to Aryabhatiya (5th century CE). A famous problem from Ganitakaumudi (14th century CE): Two postmen start walking towards each other from 210 yojanas apart. One travels 9 yojanas/day, other 5 yojanas/day. Together they cover 14 yojanas/day → 210÷14 = 15 days to meet.
📖 Definition — Average Velocity
Average velocity — Change in position (displacement) divided by the time interval. Describes how fast position is changing AND in which direction.
Eq. 4.2a & 4.2b
Average Velocity = Displacement ÷ Time Interval | vav = s / t
- SI unit of average speed AND average velocity = m s⁻¹ (m/s). Also commonly: km h⁻¹.
- Direction of velocity = same as direction of displacement (+ or − sign).
- Rate of change = ratio of change in one quantity to corresponding change in time. Average velocity = average rate of change of position with respect to time.
📝 Example 4.2 — Swimming Pool Problem
Problem: Sarang takes 50 s to swim from one end (25 m) to the other and back. Find average speed and average velocity.
Solution:
Total distance = 25 m + 25 m = 50 m | Displacement = 0 m (back to start)
Average speed = 50 m ÷ 50 s = 1 m s⁻¹
Average velocity = 0 m ÷ 50 s = 0 m s⁻¹
Key takeaway: Speed can be non-zero while velocity is zero, when object returns to starting point!
💡 Note — Important Rule
For motion in a straight line, average speed = magnitude of average velocity ONLY IF the object moves in one direction (without turning back).
🔩 Ready to Go Beyond — Scalars and Vectors
Scalars — Physical quantities specified by just numerical value (e.g., distance, speed). Vectors — Physical quantities requiring both direction and magnitude (e.g., displacement, velocity, acceleration).
💡 Instantaneous Velocity — Ready to Go Beyond
‘Velocity at an instant’ is called instantaneous velocity. As time interval becomes infinitesimally small, average velocity approaches a fixed value — the instantaneous velocity.
✅ Check Your Understanding — Speed & Velocity
Q4. Which physical quantity has NO direction, only a numerical value?
ADisplacement
BAverage speed
CAverage velocity
DAcceleration
Q5. If an object travels equal distances in equal time intervals, its motion is called:
AUniform motion
BNon-uniform motion
CCircular motion
DRandom motion
Q6. Sarang swims 25 m and back in 50 s. His average velocity is:
A1 m/s
B0 m/s
C0.5 m/s
D2 m/s
📋 Answer Key
Q4B — Average speed. Speed is a scalar (numerical value only). Displacement, velocity, acceleration are vectors (need direction too).
Q5A — Uniform motion. Equal distances in equal time intervals = constant speed = uniform motion.
Q6B — 0 m/s. Since he returns to the starting point, displacement = 0, so average velocity = 0 (though average speed = 1 m/s).
🚀 4.1.4 Average Acceleration
When a vehicle suddenly moves from rest or suddenly stops, you feel a jolt — this captures the change in velocity.
📖 Definition
Average acceleration — Change in velocity divided by the time interval over which the change occurs.
Eq. 4.3a, 4.3b, 4.3c
Average acceleration = (Final velocity − Initial velocity) ÷ Time interval
a = (v − u) ÷ (t₂ − t₁)
- SI unit of average acceleration = m s⁻² (m/s²)
- If velocity increases → acceleration is in the direction of velocity
- If velocity decreases → acceleration is opposite to direction of velocity
🎯 Exam Point — Important Misconception
An object can be moving very fast yet have zero acceleration! Acceleration depends on how quickly velocity is changing, not on how fast the object is moving. Example: A bus at constant 80 km/h has zero acceleration even though velocity is high.
📝 Example 4.3 — Bus Accelerating and Braking
Problem: Bus moving at 36 km/h. Accelerator pressed for 10s → velocity becomes 54 km/h. Then brakes applied, bus stops in 5s.
(i) When accelerator pressed:
u = 36 km/h = 10 m/s, v = 54 km/h = 15 m/s, t = 10 s
a = (15 − 10) ÷ 10 = 0.5 m s⁻² (in direction of velocity)
(ii) When brakes pressed:
u = 54 km/h = 15 m/s, v = 0 m/s, t = 5 s
a = (0 − 15) ÷ 5 = −3 m s⁻² (opposite to direction of velocity)
📝 Example 4.4 — Free Falling Object (Acceleration due to Gravity)
An object dropped from height: velocities at successive seconds: 0, 9.8, 19.6, 29.4, 39.2 m/s.
a (each interval) = (9.8 − 0)/(1−0) = 9.8 m/s² (constant in every interval!)
Conclusion: Average acceleration is constant = 9.8 m s⁻², in the direction of motion (downward). This is the acceleration due to gravity, denoted by g.
💡 Important Notes
- For an object moving in a straight line in the same direction, if velocity changes by equal amounts in equal time intervals → acceleration is constant.
- We can choose origin and positive direction as per convenience — but once chosen, should not be changed while solving a problem.
- ‘Acceleration at an instant’ = instantaneous acceleration.
🔩 Threads of Curiosity
The reading of a vehicle’s speedometer is nearly (but not exactly) the same as the magnitude of velocity at an instant, while the direction of tyres gives the direction of velocity.
🧪 Activity 4.2 — Calculating Average Acceleration of Cars
The magnitude of average acceleration of cars is specified as the time taken to go from 0 km/h to 100 km/h. Look up this time for various cars and calculate their average acceleration using a = (final velocity − initial velocity) ÷ time.
✅ Check Your Understanding — Acceleration
Q7. The SI unit of average acceleration is:
Am s⁻¹
Bm s⁻²
Cm
Ds
Q8. A bus moving at constant velocity on a straight highway has acceleration equal to:
AMaximum
BZero
CEqual to its velocity
DNegative
Q9. The acceleration due to gravity (g) is approximately:
A9.8 m/s
B9.8 m/s²
C9.8 m
D98 m/s²
📋 Answer Key
Q7B — m s⁻². Acceleration = velocity ÷ time = (m/s) ÷ s = m/s².
Q8B — Zero. Constant velocity means no change in velocity, hence zero acceleration — regardless of how fast it’s moving.
Q9B — 9.8 m/s². This is the constant acceleration experienced by objects in free fall due to Earth’s gravity.
🔑 Keywords — Part 1
Linear MotionReference PointOriginPositionIn MotionAt RestDistanceDisplacementMagnitudeScalarVectorAverage SpeedAverage VelocityUniform MotionNon-Uniform MotionRate of ChangeInstantaneous VelocityAverage AccelerationInstantaneous AccelerationAcceleration due to GravityTime IntervalInstant of Time
📖 Important Definitions — Part 1
PositionThe distance and direction of an object with respect to a reference point, at any instant of time.
DisplacementThe net change in position of an object between two given instants of time. A vector quantity with both magnitude and direction.
MagnitudeThe numerical value (with units) of a physical quantity like displacement.
Average SpeedTotal distance travelled divided by the time interval during which it is covered. A scalar quantity (no direction).
Average VelocityDisplacement divided by time interval. A vector quantity, describing how fast position changes and in which direction.
Average AccelerationChange in velocity divided by the time interval over which the change occurs.
Uniform MotionMotion where an object travels equal distances in equal time intervals. Speed is constant.
ScalarPhysical quantities specified by just numerical value (e.g., distance, speed, time).
VectorPhysical quantities requiring both magnitude and direction (e.g., displacement, velocity, acceleration).
❓ Frequently Asked Exam Concepts — Part 1
Why can speed be non-zero while velocity is zero? ▶
Speed depends on total distance travelled (always positive, accumulates). Velocity depends on displacement (net change in position). If an object returns to its starting point after travelling some distance, the total distance travelled is non-zero, but the displacement is zero (since the net change in position is zero). Example: Sarang swims 50 m total but returns to start, so average speed = 1 m/s but average velocity = 0 m/s.
Can an object have zero acceleration while moving very fast? ▶
Yes! Acceleration depends on how quickly velocity is CHANGING, not on how fast an object is moving. A car cruising at a constant 100 km/h on a straight highway has a very high speed but ZERO acceleration because its velocity isn’t changing. Acceleration only becomes non-zero when speed or direction changes.
What is the difference between distance and displacement? ▶
Distance is the total path length covered by an object — always positive, scalar (no direction). Displacement is the net change in position — a vector with both magnitude and direction, calculated as the straight-line distance from start to end position. Distance ≥ |displacement| always; they are equal only when the object moves in a single direction without turning back.
Why is acceleration due to gravity (g) considered constant? ▶
When an object falls freely, its velocity increases by the same amount (9.8 m/s) in every successive one-second interval, regardless of which interval you check. Since the rate of change of velocity is the same throughout the motion, the acceleration is constant. This constant value is denoted by g = 9.8 m/s² and acts in the direction of motion (downward, for falling objects).
📌 Continue to Part 2 →
Graphical Representation of Motion (Position-Time & Velocity-Time Graphs) · Kinematic Equations · Motion in a Plane · Uniform Circular Motion · Final Quiz