Class 11 Physics Motion in a Straight Line Notes and Questions

 

NCERT Physics Class 11 Chapter 2 Easy Line-by-Line Notes 

- Dr.Sanjaykumar pawar

Area Under Velocity-Time Graph

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Fig. 2.4 Explanation

“Area under v–t curve equals displacement...”

Very Important Concept

On a velocity-time graph:

Displacement=\text{Area under v-t graph}

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“The v–t curve is a straight line parallel to the time axis...”

Meaning

• Velocity remains constant.

• Object moves with uniform velocity.

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“Area under it between t = 0 and t = T is the area of rectangle...”

Graph Shape

Rectangle:

• Height = velocity (u)

• Base = time (T)

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Rectangle Area

Area=u\times T

Since:

• area under graph = displacement

Therefore:

x=uT

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“How come area equals distance?”

Dimensional Understanding

Velocity × Time:

[
(m/s)\times s = m
]

So result becomes displacement.

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Important Note About Graphs

“x–t, v–t and a–t graphs shown have sharp kinks...”

Meaning

Some graphs in textbooks have sharp corners.

But in real life:

• motion changes smoothly.

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“Acceleration and velocity cannot change abruptly...”

Important Physical Meaning

Objects cannot instantly jump from:

• slow to very fast

• or stop suddenly

Changes are continuous.

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2.4 Kinematic Equations for Uniformly Accelerated Motion

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“For uniformly accelerated motion...”

Meaning

Acceleration remains constant.

Example:

• freely falling object

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Variables Used

Symbol	Meaning
(x)	displacement
(t)	time
(v_0)	initial velocity
(v)	final velocity
(a)	acceleration

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First Equation of Motion

“Equation already obtained gives relation between final and initial velocities...”

v=v_0+at

Meaning

Final velocity:

initial velocity + change due to acceleration

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Graphical Representation

“This relation is graphically represented in Fig. 2.5.”

Meaning

Velocity-time graph becomes a straight line.

Reason:

• acceleration is constant.

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Area Under Graph

“Area between instants 0 and t = area of triangle + rectangle”

Total displacement:

=
rectangle area + triangle area

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Second Equation of Motion

Meaning

Displacement depends on:

• initial velocity

• acceleration

• time

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Average Velocity Form

Meaning

For constant acceleration:

Average velocity

mean of initial and final velocities.

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Important Condition

“Constant acceleration only”

This formula works only when:

• acceleration remains constant.

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Third Equation of Motion

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Meaning of Third Equation

This equation connects:

• velocity

• displacement

• acceleration

without using time.

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Three Main Equations of Motion

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Graph Concepts Summary

Graph	Slope Gives	Area Gives
Position-Time	Velocity	—
Velocity-Time	Acceleration	Displacement

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Real-Life Examples

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One-Line Summary

For uniformly accelerated motion, displacement and velocity can be calculated using three important equations derived from the velocity-time graph. 

KINEMATIC EQUATIONS FOR UNIFORMLY ACCELERATED MOTION

│

├── Velocity-Time Graph

│   ├── Area under graph = displacement

│   ├── Constant velocity graph

│   │   └── Horizontal straight line

│   └── Uniform acceleration graph

│       └── Sloping straight line

│

├── Area Under v-t Graph

│   ├── Rectangle area

│   │     displacement = velocity × time

│   ├── Formula

│   │     x = uT

│   └── Unit check

│         (m/s) × s = m

│

├── Important Physical Idea

│   ├── Velocity changes continuously

│   ├── Acceleration changes continuously

│   └── Real motion graphs are smooth

│

├── Uniformly Accelerated Motion

│   ├── Constant acceleration

│   └── Variables

│       ├── x → displacement

│       ├── t → time

│       ├── v₀ → initial velocity

│       ├── v → final velocity

│       └── a → acceleration

│

├── First Equation of Motion

│   ├── Formula

│   │     v = v₀ + at

│   ├── Gives final velocity

│   └── Used when time is known

│

├── Displacement from Graph

│   ├── Total area

│   │     = rectangle + triangle

│   │

│   ├── Rectangle area

│   │     = v₀t

│   │

│   ├── Triangle area

│   │     = 1/2 (v - v₀)t

│   │

│   └── Total displacement

│         x = v₀t + 1/2 (v - v₀)t

│

├── Second Equation of Motion

│   ├── Using

│   │     v - v₀ = at

│   ├── Formula

│   │     x = v₀t + 1/2 at²

│   └── Used for displacement

│

├── Average Velocity

│   ├── Formula

│   │     v_avg = (v + v₀)/2

│   ├── Works only for constant acceleration

│   └── Displacement form

│         x = [(v + v₀)/2] t

│

├── Third Equation of Motion

│   ├── Formula

│   │     v² = v₀² + 2ax

│   ├── Time not required

│   └── Relates

│       ├── velocity

│       ├── displacement

│       └── acceleration

│

├── Three Main Equations

│   │

│   ├── First

│   │     v = v₀ + at

│   │

│   ├── Second

│   │     x = v₀t + 1/2 at²

│   │

│   └── Third

│         v² = v₀² + 2ax

│

├── Graph Rules

│   ├── Position-Time Graph

│   │   └── Slope = velocity

│   │

│   └── Velocity-Time Graph

│       ├── Slope = acceleration

│       └── Area = displacement

│

├── Real-Life Examples

│   ├── Accelerating car

│   ├── Falling object

│   ├── Braking vehicle

│   └── Train gaining speed

│

└── Key Ideas

    ├── Constant acceleration simplifies motion

    ├── Area under v-t graph gives displacement

    └── Equations of motion describe straight-line motion 

Internal Links

1. Class 11 Physics Units and Measurements Notes
2. Class 11 Physics Laws of Motion Notes
3. Class 11 Physics Work Energy and Power Questions
4. Kinematics Formula Sheet PDF
5. CBSE Class 11 Physics Important Numericals
6. Class 11 Physics Chapter Wise MCQs
7. Motion in a Plane Complete Notes
8. Physics Graphs and Derivations Guide
9. NCERT Solutions for Class 11 Physics
10. Physics Assertion Reason Questions Collection

CBSE Class 11 Physics Question Bank

Chapter: Motion in a Straight Line

1. Multiple Choice Questions (MCQs)

1. Motion is defined as:

• A. Change in mass
• B. Change in position with time
• C. Change in force
• D. Change in shape

Answer: B. Change in position with time

2. SI unit of acceleration is:

• A. m/s
• B. m/s²
• C. km/h
• D. m²/s

Answer: B. m/s²

3. Area under velocity-time graph gives:

• A. Velocity
• B. Acceleration
• C. Displacement
• D. Speed

Answer: C. Displacement

2. Very Short Answer Questions

1. Define motion.

Motion is the change in position with time.

2. Define acceleration.

Acceleration is the rate of change of velocity with time.

3. Write SI unit of velocity.

m/s

3. Short Answer Questions

1. Differentiate between speed and velocity.

Speed	Velocity
Scalar quantity	Vector quantity
No direction	Has direction
Only magnitude	Magnitude and direction

2. Write formula of average velocity.

v = Δx / Δt

Average velocity is displacement divided by time.

4. Long Answer Questions

1. Derive second equation of motion.

v = u + at

s = ut + 1/2 at²

The second equation of motion is obtained from velocity-time graph by calculating area under the graph.

5. Assertion and Reason Questions

Assertion: Slope of velocity-time graph gives acceleration.
Reason: Acceleration is rate of change of velocity with time.

Both Assertion and Reason are true and Reason correctly explains Assertion.

Assertion: Speed can be negative.
Reason: Speed is scalar quantity.

Assertion is false but Reason is true.

6. Fill in the Blanks

1. Motion is change in ______ with time.

position

2. SI unit of acceleration is ______.

m/s²

3. Area under velocity-time graph gives ______.

displacement

7. Statement Based Questions

Statement I: Velocity has direction.
Statement II: Speed has no direction.

Both statements are true.

Statement I: Uniform motion means constant velocity.
Statement II: Acceleration is zero in uniform motion.

Both statements are true.

8. Match the Columns

Column A	Column B
Slope of x-t graph	Velocity
Slope of v-t graph	Acceleration
Area under v-t graph	Displacement
Constant velocity	Zero acceleration

9. Case Study Questions

A car starts from rest and accelerates uniformly at 2 m/s² for 5 seconds.

1. Find final velocity.
2. Find displacement.

v = u + at

v = 0 + (2)(5) = 10 m/s

s = ut + 1/2 at²

s = 0 + 1/2(2)(25) = 25 m

Final velocity = 10 m/s
Displacement = 25 m

10. Important Formulas

v = u + at

s = ut + 1/2 at²

v² = u² + 2as

a = (v - u)/t

Class 11 Physics Motion in a Straight Line notes, formulas, graphs, and important CBSE exam questions.