Motion in One Dimension

Introduction

Motion is a fundamental concept in physics. When an object moves along a straight line, it is said to be in one-dimensional motion. ICSE Class 9 covers the basic parameters of motion and the equations that describe uniformly accelerated motion.

Basic Concepts

Distance and Displacement

Parameter	Distance	Displacement
Definition	Total path length	Shortest straight-line distance from start to end
Scalar/Vector	Scalar	Vector
Value	Always positive	Positive, negative, or zero
Dependence	Depends on path	Independent of path

Speed and Velocity

Parameter	Speed	Velocity
Definition	Distance/time	Displacement/time
Scalar/Vector	Scalar	Vector
Formula	Speed = Distance/Time	Velocity = Displacement/Time

Acceleration

Acceleration = Change in velocity / Time taken = (v - u)/t

Unit: m/s²

Positive acceleration: velocity increases with time
Negative acceleration (retardation/deceleration): velocity decreases with time
Zero acceleration: uniform velocity

Distance-Time and Speed-Time Graphs

Distance-Time Graph

Straight line through origin: Uniform speed
Horizontal line: Object at rest
Curved line: Non-uniform speed
Slope = speed

Speed-Time Graph

Horizontal line: Uniform acceleration
Straight line through origin: Uniform acceleration starting from rest
Area under graph: Distance travelled
Slope = acceleration

<ICSEExample title="Interpret Speed-Time Graph"> A car accelerates uniformly from rest to 20 m/s in 10 s and then travels at constant speed for 20 s. Draw the speed-time graph and find total distance. <Solution> Distance = Area under graph = Area of triangle + Area of rectangle = 1/2 × 10 × 20 + 20 × 20 = 100 + 400 = 500 m </Solution> </ICSEExample>

Equations of Motion

For uniformly accelerated motion:

v = u + at
s = ut + 1/2 × at²
v² = u² + 2as

Where:

u = initial velocity (m/s)
v = final velocity (m/s)
a = acceleration (m/s²)
t = time (s)
s = displacement (m)

<ICSEExample title="Using Equations of Motion"> A car starts from rest and accelerates at 2 m/s² for 5 seconds. Find its velocity and distance travelled. <Solution> u = 0 m/s, a = 2 m/s², t = 5 s v = u + at = 0 + 2×5 = 10 m/s s = ut + 1/2 × at² = 0 + 1/2 × 2×25 = 25 m </Solution> </ICSEExample> <ICSEExample title="Finding Deceleration"> A car moving at 20 m/s comes to rest after travelling 50 m. Find the deceleration. <Solution> u = 20 m/s, v = 0 m/s, s = 50 m v² = u² + 2as 0 = 400 + 2×a×50 100a = -400 a = -4 m/s² (deceleration of 4 m/s²) </Solution> </ICSEExample>

Free Fall

Free fall is the motion of an object under the influence of gravity only.

For free fall:

a = g = 9.8 m/s² (downward)
u = 0 (if dropped from rest)

<ICSEExample title="Free Fall"> A stone is dropped from a height of 80 m. Find the time taken to reach the ground and the velocity on impact. (g = 10 m/s²) <Solution> u = 0, s = 80 m, a = 10 m/s² s = ut + 1/2 × at² 80 = 0 + 1/2 × 10 × t² 80 = 5t² t² = 16 t = 4 s

v = u + at = 0 + 10×4 = 40 m/s </Solution> </ICSEExample>

Common Mistakes With Fixes

Mistake	Correction
Confusing distance and displacement	Distance is total path length; displacement is straight-line
Using equations of motion for non-uniform acceleration	Equations of motion apply ONLY for uniform acceleration
Wrong sign convention for free fall	Downward direction is usually positive for free fall
Forgetting units in calculations	Always include units (m, s, m/s, m/s²)

ICSE Exam Focus

Topic	Marks (approx.)	Frequency
Equations of motion numerical	4-5 marks	Very common
Distance-time and speed-time graphs	4 marks	Common
Free fall problems	3-4 marks	Very common
Distinguishing scalar and vector quantities	2-3 marks	Common

Self-Test

Q1: A car accelerates from 10 m/s to 25 m/s in 5 s. Find the acceleration and distance covered.

Q2: A ball is thrown vertically upwards with a velocity of 30 m/s. Find the maximum height reached. (g = 10 m/s²)

Q3: Distinguish between speed and velocity.

Q4: A train travelling at 72 km/h comes to rest in 10 s. Find the retardation.

Q5: From the speed-time graph of a body, the area under the curve gives what physical quantity?

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