Uniformly Accelerated Motion Class 11 Physics Notes | NEET & JEE MCQs

 - Dr.Sanjaykumar Pawar  

Uniformly Accelerated Motion (1-D) Physics Notes, Formulas & NEET Questions 

Uniformly Accelerated Motion (1-D): Equations of Motion, Graphs and NEET Physics Concepts

Internal Links

1. Motion in One Dimension Foundation

 Motion in One Dimension Class 11 Physics Notes

Before introducing uniformly accelerated motion, link readers to the basic concepts of displacement, velocity and speed.

2. Instantaneous Velocity & Acceleration

Instantaneous Velocity and Acceleration Explained

NCERT Physics Class 11 Chapter 2: Instantaneous Velocity & Acceleration

Under "Important Terms" section after explaining acceleration.

3. Vectors in Physics

Vectors Class 11 Physics Notes

CBSE Class 11 Physics Vectors Notes, MCQs, Questions & Answers | NEET Preparation

  explaining displacement as a vector quantity.

4. Newton's Laws of Motion

Newton's Laws of Motion Class 11 Physics

Block and Trolley System NEET Solution | Acceleration & Tension Explained

acceleration concepts because force causes acceleration.

5. Free Fall Motion

Free Fall and Acceleration Due to Gravity

NEET Tips section where free fall problems are mentioned.

6. Graphical Motion Analysis

Velocity-Time and Acceleration-Time Graphs

 diagram-based questions.

Uniform acceleration formula

Equations of motion derivation

Motion in one dimension notes

Class 11 Physics chapter 2 notes

NEET physics motion questions

JEE physics kinematics notes

Velocity time graph questions

Acceleration numericals with solutions

CBSE Physics important questions

Physics revision notes for NEET

FAQ Schema Questions

Q1. What is uniformly accelerated motion?

Uniformly accelerated motion is motion in which acceleration remains constant with time.

Q2. What are the three equations of motion?

The three equations are v = u + at, s = ut + ½at² and v² = u² + 2as.

Q3. What does the slope of a velocity-time graph represent?

The slope of a velocity-time graph represents acceleration.

Q4. What does the area under a velocity-time graph represent?

The area represents displacement.

Q5. Is uniformly accelerated motion important for NEET and JEE?

Yes, it is a fundamental topic used in many mechanics problems.

Uniformly Accelerated Motion (1-D)

1. Meaning of Uniformly Accelerated Motion

Uniformly accelerated motion means an object is moving in a straight line and its acceleration remains constant with time.

• The velocity changes by the same amount in equal intervals of time.
• The motion takes place in one dimension.

Example: A bike increases its speed by 5 m/s every second.

Important Terms

1. Initial Velocity (u)

Initial velocity is the velocity of an object at the starting time. It is represented by u.

At starting time:
t = 0, velocity = u

2. Final Velocity (v)

Final velocity is the velocity of an object after a certain time. It is represented by v.

3. Acceleration (a)

Acceleration is the rate of change of velocity.

a = (v - u) / t

Unit of acceleration = m/s²

4. Displacement (s)

Displacement is the distance travelled by an object in a particular direction.

Unit = metre (m)

First Equation of Motion

v = u + at

Derivation:

Acceleration:

a = dv/dt

Rearranging:

a dt = dv

Integrating:

∫a dt = ∫dv

a(t - 0) = v - u

at = v - u

v = u + at

Final velocity = Initial velocity + Change in velocity

Second Equation of Motion

s = ut + 1/2 at²

Derivation:

Velocity:

v = ds/dt

Therefore:

ds = v dt

Using:
v = u + at

ds = (u + at)dt

After integration:

s = ut + 1/2 at²

Displacement = Distance due to initial velocity + Distance due to acceleration

Third Equation of Motion

v² = u² + 2as

Derivation:

From first equation:

v = u + at

Rearranging:

t = (v - u)/a

Using second equation:

s = ut + 1/2 at²

After simplification:

v² = u² + 2as

This equation is useful when time is not given.

Three Equations of Motion Summary

1. Velocity Equation

v = u + at

Used to find final velocity when time is given.

2. Displacement Equation

s = ut + 1/2 at²

Used to find displacement when time is given.

3. Time Independent Equation

v² = u² + 2as

Used when time is not given.

Easy Memory Trick

• V-U-AT: v = u + at
• S-U-T-A-T: s = ut + 1/2 at²
• V-U-AS: v² = u² + 2as

Symbols at a Glance

Symbol	Meaning	Unit
u	Initial Velocity	m/s
v	Final Velocity	m/s
a	Acceleration	m/s²
t	Time	second
s	Displacement	metre

Conclusion

The three equations of motion are used to solve problems involving constant acceleration in one-dimensional motion.

NEET Physics Practice Questions

Chapter: Uniformly Accelerated Motion (1-D)

NEET Question Types

• Direct MCQs (Single Correct Option)
• Statement Based Questions
• Assertion and Reason
• Match the Columns
• Diagram Based / Graphical Questions

PART 1: Direct MCQs (Single Correct Option)

Q1. A car starts from rest and accelerates uniformly at 4 m/s². Its velocity after 5 seconds will be:

A) 10 m/s
B) 20 m/s
C) 25 m/s
D) 40 m/s

Solution:
u = 0
a = 4 m/s²
t = 5 s

v = u + at
v = 0 + 4 × 5
v = 20 m/s

Answer: B) 20 m/s

Q2. The SI unit of acceleration is:

A) m/s
B) m²/s
C) m/s²
D) km/h

Answer: C) m/s²

Q3. A body moving with velocity 20 m/s is brought to rest in 5 seconds. The acceleration is:

A) +4 m/s²
B) -4 m/s²
C) +5 m/s²
D) -5 m/s²

a = (v-u)/t
a = (0-20)/5
a = -4 m/s²

Answer: B) -4 m/s²

Q4. The velocity-time graph for uniformly accelerated motion is:

A) Straight line
B) Circle
C) Parabola
D) Hyperbola

Answer: A) Straight line

Q5. A particle starts from rest and travels 100 m in 5 seconds with uniform acceleration. Find acceleration.

A) 4 m/s²
B) 6 m/s²
C) 8 m/s²
D) 10 m/s²

s = ut + 1/2 at²
100 = 0 + 1/2 × a × 25
a = 8 m/s²

Answer: C) 8 m/s²

PART 2: Statement Based Questions

Options:
A) Both statements true and II explains I
B) Both true but II does not explain I
C) I true, II false
D) I false, II true

Q6.

Statement I: Velocity-time graph for uniformly accelerated motion is a straight line.

Statement II: Acceleration is constant in uniformly accelerated motion.

Answer: A

Q7.

Statement I: Displacement can be zero even if distance travelled is not zero.

Statement II: Displacement depends only on initial and final position.

Answer: A

Q8.

Statement I: Acceleration due to gravity is constant near Earth's surface.

Statement II: Value of g is approximately 9.8 m/s².

Answer: A

PART 3: Assertion and Reason

Options:
A) Both true and R explains A
B) Both true but R does not explain A
C) A true, R false
D) A false, R true

Q9.

Assertion: A body moving with constant velocity has zero acceleration.

Reason: Acceleration is the rate of change of velocity.

Answer: A

Q10.

Assertion: Area under velocity-time graph gives displacement.

Reason: Velocity is displacement divided by time.

Answer: A

Q11.

Assertion: A body can have zero velocity and non-zero acceleration.

Reason: At highest point of upward motion, velocity is zero but acceleration acts downward.

Answer: A

PART 4: Match the Columns

Column I	Column II
Velocity	m/s
Acceleration	m/s²
Displacement	m
Time	second

Answer: Velocity-m/s, Acceleration-m/s², Displacement-m, Time-second

PART 5: Diagram Based / Graphical Questions

Q14. The slope of velocity-time graph represents:

A) Distance
B) Velocity
C) Acceleration
D) Displacement

Answer: C) Acceleration

Q15. Area under velocity-time graph represents:

A) Acceleration
B) Displacement
C) Force
D) Momentum

Answer: B) Displacement

Q16. Velocity-time graph:

v
|
|        /
|       /
|      /
|_____/________ t

The particle has:

A) Constant velocity
B) Constant acceleration
C) Zero acceleration
D) Variable acceleration

Answer: B) Constant acceleration

Hard Numerical Practice

Q17. A train moving at 72 km/h stops in 10 seconds. Find retardation.

72 km/h = 20 m/s a = (0-20)/10 a = -2 m/s² Retardation = 2 m/s²

Q18. A particle has initial velocity 5 m/s and acceleration 2 m/s². Find distance in 10 seconds.

s = ut + 1/2at² s = 5×10 + 1/2×2×100 s = 150 m Answer: 150 m

NEET Formula Revision

v = u + at

s = ut + 1/2 at²

v² = u² + 2as

s = ((u+v)/2)t

NEET Tips

• Practice velocity-time graphs.
• Remember sign convention.
• Understand distance and displacement difference.
• Use correct equation according to given data.
• Practice free fall problems.

Work, Energy and Power Notes for NEET: Kinetic Energy & Variable Force

-  Dr.Sanjaykumar Pawar 

Kinetic Energy and Work Done by Variable Force explained with formulas, examples, and graphical interpretation for NEET aspirants.

INTERNAL LINK SUGGESTIONS

6. Laws of Motion Complete Notes

7. Motion in One Dimension Notes

8. Motion in a Plane Notes

9. Work Energy Theorem Explained

10. Potential Energy Notes

11. Conservation of Energy Notes

12. Power Formula and Applications

13. Mechanical Energy Examples

14. NCERT Physics Class 11 Solutions

15. NEET Physics Formula Sheet

16. Rotational Motion Notes

17. Gravitation Complete Notes

18. Oscillations and SHM Notes

19. Units and Measurements Notes

20. NEET Physics MCQs with Answers 

FAQ QUESTIONS

Q1. What is kinetic energy?

A. Kinetic energy is the energy possessed by a body due to its motion.

Q2. What is the formula of kinetic energy?

A. K = 1/2 mv².

Q3. What is work done by a variable force?

A. Work done by a variable force equals the area under the force-displacement graph.

Q4. Why is speed not reduced by 90% when kinetic energy becomes 10%?

A. Because kinetic energy is proportional to the square of speed.

Q5. What is the SI unit of work?

A. Joule (J).

WORK, ENERGY AND POWER

1. Kinetic Energy (K)

Kinetic energy is the energy possessed by a body due to its motion.

K = ½ mv²

Where:

• m = mass of the object
• v = speed of the object
• K = kinetic energy

2. Typical Kinetic Energies

Object	Mass (kg)	Speed (m/s)	Kinetic Energy (J)
Car	2000	25	6.3 × 10⁵
Running Athlete	70	10	3.5 × 10³
Bullet	0.05	200	10³
Stone Dropped from 10 m	-	14	10²
Rain Drop	3.5 × 10⁻⁵	9	1.4 × 10⁻³
Air Molecule	≈ 10⁻²⁶	500	≈ 10⁻²¹

Heavy objects moving fast possess very large kinetic energy.

3. Example: Bullet Passing Through Plywood

Given:

• Mass of bullet = 50 g = 0.05 kg
• Initial speed = 200 m/s
• Final kinetic energy = 10% of initial kinetic energy

Step 1: Initial Kinetic Energy

Ki = ½mv²

Ki = ½ × 0.05 × (200)²

Ki = 1000 J

Step 2: Final Kinetic Energy

Kf = 10% of 1000

Kf = 100 J

Step 3: Calculate Final Speed

½mvf² = 100

vf = √(2 × 100 / 0.05)

vf = 63.2 m/s

Answer: Emergent speed = 63.2 m/s

4. Important Concept for NEET

Kinetic Energy is proportional to the square of speed.

K ∝ v²

If kinetic energy becomes 10%:

vf = √0.1 × vi

vf = 0.316 × vi

Speed becomes 31.6% of original speed.

Reduction in speed:

100 − 31.6 = 68.4%

Speed is reduced by approximately 68%, not 90%.

5. Work Done by a Variable Force

Constant Force

A constant force is a force whose magnitude and direction remain unchanged.

Examples:

• Weight of a body near Earth
• Pushing a box with constant force

W = F × s

Where:

• W = Work Done
• F = Force
• s = Displacement

Variable Force

A variable force changes with position, time, or direction.

Examples:

• Spring Force
• Gravitational Force
• Electric Force

For variable force, W = Fs cannot be directly used.

6. Small Displacement Method

Consider a very small displacement Δx.

Over this tiny distance, force can be treated as constant.

ΔW = F(x)Δx

Where:

• ΔW = Small work done
• F(x) = Force at position x
• Δx = Small displacement

7. Total Work Done

Adding work done over many small intervals:

W = Σ F(x)Δx

This is called summation.

Meaning:

• Divide motion into many small parts.
• Find work done in each part.
• Add all the small works.

8. Graphical Interpretation

In a Force vs Position graph:

• Y-axis → Force F(x)
• X-axis → Position x

Area of one small rectangle:

ΔA = F(x)Δx

Since:

ΔW = F(x)Δx

Therefore:

ΔW = ΔA

Small Work Done = Area of Small Rectangle

9. Integral Form of Work Done

When Δx becomes extremely small:

W = ∫ F(x) dx

Limits:

W = ∫_xi^xf F(x) dx

Where:

• xi = Initial Position
• xf = Final Position

Work Done by Variable Force = Area Under Force-Position Curve

10. NEET Quick Revision

Kinetic Energy

K = ½mv²

• KE ∝ Mass
• KE ∝ Speed²

If Speed Doubles

K → 4K

If Speed Triples

K → 9K

Variable Force

ΔW = F(x)Δx

W = ΣF(x)Δx

W = ∫F(x)dx

Most Important NEET Statement

✔ Work Done = Area under Force-Displacement Graph

Frequently Asked Relation

If KE becomes n times:

v = √n × Initial Speed

If speed becomes n times:

K = n² × Initial Kinetic Energy

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CBSE Class 11 Physics Question Bank

Chapter: Work, Energy and Power

Section A: Very Short Answer Questions (1 Mark)

1. Define kinetic energy.

Kinetic energy is the energy possessed by a body due to its motion.

2. Write the SI unit of kinetic energy.

Joule (J)

3. Write the formula for kinetic energy.

K = ½mv²

4. On what factors does kinetic energy depend?

Mass and square of velocity.

5. What is the kinetic energy of a body at rest?

Zero.

6. What is a variable force?

A force whose magnitude changes with position is called a variable force.

7. Write the expression for small work done by a variable force.

ΔW = F(x)Δx

8. What does the area under an F-x graph represent?

Work done by the force.

9. What is the SI unit of work?

Joule (J)

10. Write the integral form of work done.

W = ∫F(x)dx

Section B: Short Answer Questions (2 Marks)

1. Why does a bullet possess large kinetic energy despite having small mass?

A bullet has very high speed. Since kinetic energy depends on the square of velocity, it possesses large kinetic energy.

2. Calculate the kinetic energy of a body of mass 4 kg moving with speed 5 m/s.

K = ½mv²
= ½ × 4 × 25
= 50 J

3. Distinguish between constant force and variable force.

Constant Force	Variable Force
Remains unchanged	Changes with position
W = Fs	W = ∫Fdx
Example: Weight	Example: Spring Force

4. State the graphical interpretation of work done.

Work done by a force is equal to the area under the force-displacement graph.

5. If velocity doubles, how does kinetic energy change?

K ∝ v²
Therefore kinetic energy becomes four times.

Section C: Long Answer Questions (5 Marks)

1. Derive the expression for kinetic energy.

Work done W = Fs

Using F = ma
W = mas

Using equation of motion:
v² − u² = 2as
a = (v² − u²)/2s

Substituting:
W = m(v² − u²)/2

For u = 0:
K = ½mv²

2. Explain work done by a variable force with graphical interpretation.

For a small displacement Δx:
ΔW = F(x)Δx

Adding all small works:
W = ΣF(x)Δx

As Δx approaches zero:
W = ∫F(x)dx

Thus, work done by a variable force equals the area under the force-displacement graph.

Section D: Multiple Choice Questions

1. Kinetic energy depends on:

• A. Mass only
• B. Velocity only
• C. Mass and velocity
• D. Mass and square of velocity

Answer: D

2. SI unit of kinetic energy is:

• A. Newton
• B. Joule
• C. Watt
• D. Pascal

Answer: B

3. If speed triples, kinetic energy becomes:

• A. 3 times
• B. 6 times
• C. 9 times
• D. 27 times

Answer: C

4. Area under force-displacement graph represents:

• A. Velocity
• B. Momentum
• C. Work done
• D. Acceleration

Answer: C

Section E: Assertion and Reason

Assertion (A): Kinetic energy is proportional to square of velocity.
Reason (R): K = ½mv².

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

Assertion (A): Area under force-displacement graph gives work done.
Reason (R): ΔW = FΔx.

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

Section F: Fill in the Blanks

1. Kinetic energy is measured in Joule.
2. The formula of kinetic energy is ½mv².
3. Work done by variable force equals the area under F-x graph.
4. Kinetic energy is proportional to the square of velocity.
5. The SI unit of work is Joule.

Section G: Match the Columns

Column A	Column B
Kinetic Energy	Energy due to motion
Joule	Unit of work
Variable Force	Spring force
Area under F-x graph	Work done

Correct Matching:
A → Energy due to motion
B → Unit of work
C → Spring force
D → Work done

Section H: Statement Based Questions

Statement I: A bullet moving at high speed possesses kinetic energy.
Statement II: Kinetic energy depends on square of velocity.

Both statements are true.

Section I: Case Study Questions

A bullet of mass 0.05 kg is fired with speed 200 m/s. After passing through a wooden block, it retains only 10% of its original kinetic energy.

1. What is the initial kinetic energy?

1000 J

2. What is the final kinetic energy?

100 J

3. What is the final speed?

63.2 m/s

4. Is speed reduced by 90%?

No.

5. Why?

Because kinetic energy is proportional to velocity squared.

Section J: Competency Based Questions

1. A car moving at 20 m/s has kinetic energy K. If its speed becomes 40 m/s, what will be its kinetic energy?

K' = (40/20)² K = 4K

2. Why does a fast-moving cricket ball hurt more than a slow-moving ball?

A fast-moving ball possesses greater kinetic energy because kinetic energy depends on the square of speed.

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What is Physics? | Physical World Class 11 Notes & Origins

Understanding the roots of Science and Physics helps us decode the mysteries of the universe. 

 Internal Links

 * The Scientific Method: 5 Steps to Discovery

 * Fundamental Forces of Nature: From Gravity to Nuclear

 * Units and Measurements: The Language of Physics

 * Great Physicists Who Changed the World

Would you like me to generate the content for a "Fundamental Forces" section to link to next? 

-Dr.Sanjaykumar pawar

 wed25March9:30p.m

Chapter 1: The Physical World

What is Science?

Science is a systematic attempt to understand natural phenomena in as much detail and depth as possible. We use the knowledge gained from this study to:

• Predict: Anticipate what will happen.
• Modify: Change certain conditions.
• Control: Manage the outcome of phenomena.

Language	Word	Meaning
Latin	Scientia	To know
Sanskrit	Vijnan	Knowledge
Arabic	Ilm	Knowledge

---

What is Physics?

"Physics is a study of the basic laws of nature and its manifestation in different natural phenomena."

Physics helps us understand how the universe behaves, from the smallest particles to the largest galaxies.

Etymology of Physics:

• Greek Origin: Derived from the word "Fusis", which signifies Nature.
• Sanskrit Equivalent: The word "Bhautiki" is used to refer to the study of the physical world.

Visualizing the Physical World

A breakdown of the definitions and origins of our understanding of nature.

The Concept of Science

From Latin "Scientia"

It is the process of gathering knowledge to understand the 'why' behind everything.

The Concept of Physics

From Greek "Fusis"

It is the study of the actual laws that govern the behavior of the material universe.

Linguistic Mapping (Real Data)

Subject	Root Word	Origin Language	Core Meaning
Science	Scientia	Latin	To Know / Knowledge
Physics	Physis / Fusis	Ancient Greek	Nature
Vijnan	Vijnana	Sanskrit	Discerning Knowledge
Bhautiki	Bhuta	Sanskrit	Physical / Material World

The Goal of Scientific Study

We don't just learn for the sake of it. Science follows a specific functional path:

Predict

→

Modify

→

Control

Explanation:
1. Predict: Use math to guess future events (like an eclipse).
2. Modify: Change variables to see different results.
3. Control: Use the laws to build technology (like using gravity for satellites).

Physical World: Practice Set

Section A: Multiple Choice Questions (NEET Pattern)

NEET / AIIMS

Q1. The word 'Physics' comes from the Greek word 'Fusis' which means:

• A) Knowledge
• B) Nature
• C) Matter
• D) Motion

View Solution

Correct Answer: B
Explanation: The term originates from the Greek 'Physis' (Fusis), signifying nature.

Section B: Assertion and Reason

CBSE 2026 Pattern

Assertion (A): Science is ever-evolving and no theory is final.

Reason (R): New observations and experiments may lead to modifications of existing laws.

View Solution

Answer: Both (A) and (R) are true and (R) is the correct explanation of (A).

Section C: Very Short Answer Questions (1 Mark)

Q2. What is the meaning of the Sanskrit word 'Vijnan'?

View Solution

Answer: It means 'Knowledge'.

Section D: Short Answer Questions (2-3 Marks)

Q3. Distinguish between the scope of Classical Physics and Quantum Physics.

View Solution

Classical Physics deals with macroscopic phenomena (large scale), while Quantum Physics deals with microscopic phenomena at the atomic and molecular level.

Section E: Long Answer Questions (5 Marks)

Q4. Explain the systematic steps involved in the 'Scientific Method'.

View Solution

1. Systematic Observations
2. Controlled Experiments
3. Qualitative and Quantitative Reasoning
4. Mathematical Modeling
5. Prediction and Verification/Falsification of Theories