Kinematic Equations of Motion | NEET & Class 11 Physics Notes (Complete Guide)

KINEMATIC EQUATIONS FOR UNIFORMLY ACCELERATED MOTION

NEET Physics Easy Notes

1. Area under v–t Graph = Displacement

Fig. 2.4 Explanation

• Velocity–time graph is a straight horizontal line.
• Horizontal line means velocity is constant.
• Time is shown on x-axis.
• Velocity is shown on y-axis.

The shaded area forms a rectangle.

Rectangle dimensions:

• Height = velocity = (u)
• Base = time = (T)

Area = u × T

Since area under velocity-time graph gives displacement,

x = uT

Important Point

• Area under v–t graph always gives displacement.
• Unit check:

(velocity) × (time) = m/s × s = m

So result is displacement.

2. Real Graphs are Smooth

Book Note Meaning

• Some graphs show sharp corners.
• In reality, velocity and acceleration do not change suddenly.
• Physical quantities change continuously.

NEET Point

• Real motion graphs are smooth curves.
• Sudden jumps are not realistic.

3. Uniformly Accelerated Motion

Uniform acceleration means:

• Acceleration remains constant throughout motion.

Main Quantities

• (u) = initial velocity
• (v) = final velocity
• (a) = acceleration
• (t) = time
• (x) = displacement

4. First Equation of Motion

Relationship between velocity and time:

v = u + at

Meaning

• Final velocity increases uniformly with time.
• Every second velocity changes by (a).

Rearranged Forms

a = (v - u)/t

t = (v - u)/a

NEET Tip

Use when:

• time is involved
• displacement is NOT required

5. Derivation of Second Equation of Motion

Step 1: Area under v–t graph

Displacement = area of rectangle + area of triangle

Rectangle Area

• Height = (u)
• Base = (t)

Rectangle Area = ut

Triangle Area

• Height = (v - u)
• Base = (t)

Triangle Area = 1/2 (v - u)t

Total Displacement

x = ut + 1/2 (v - u)t

From first equation:

v - u = at

Substitute:

x = ut + 1/2 at²

6. Second Equation Meaning

• Object already moves with initial velocity (u).
• Additional displacement comes due to acceleration.

Special Case

If object starts from rest:

u = 0

Then,

x = 1/2 at²

7. Third Equation of Motion

Using:

t = (v - u)/a

and substituting into displacement equation:

We get:

v² = u² + 2ax

8. Third Equation Meaning

• Connects velocity and displacement directly.
• Time is absent.

NEET Tip

Use when:

• time is NOT given
• displacement, velocity and acceleration are given

9. Average Velocity Formula

For constant acceleration:

v̄ = (u + v)/2

Displacement:

x = v̄t

So,

x = (u + v)t / 2

10. Important NEET Formula Sheet

Concept	Formula
First Equation	v = u + at
Second Equation	x = ut + 1/2 at²
Third Equation	v² = u² + 2ax
Average Velocity	v̄ = (u + v)/2

11. Quick Concept Tricks for NEET

If acceleration is zero

a = 0

Then:

v = u

Motion becomes uniform motion.

If object starts from rest

u = 0

Equations become:

v = at

x = 1/2 at²

v² = 2ax

12. Graph-Based NEET Concepts

Velocity-Time Graph

• Slope = acceleration
• Area under graph = displacement

Acceleration-Time Graph

• Area under graph = change in velocity

Displacement-Time Graph

• Slope = velocity

13. Most Important NEET Mistakes

❌ Using km/h instead of m/s

❌ Forgetting sign of acceleration

❌ Using wrong equation

❌ Taking displacement as distance

❌ Forgetting (u = 0) for rest condition

14. One-Line Revision

• Area under v–t graph → displacement
• Slope of v–t graph → acceleration
• Constant acceleration → use equations of motion
• Average velocity in uniform acceleration:

(u + v)/2

NEET Physics Easy Notes © 2026

- Dr.Sanjaykumar Pawar  

CBSE Class 11 Physics: Kinematics (Uniformly Accelerated Motion)

Complete Question Bank with Answers

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Very Short Answer Questions (1 Mark)

Q1. What is uniform acceleration?
Ans: Uniform acceleration is acceleration that remains constant throughout the motion.

Q2. What is SI unit of acceleration?
Ans: m/s²

Q3. What does slope of velocity-time graph represent?
Ans: Acceleration

Q4. What does area under velocity-time graph represent?
Ans: Displacement

Q5. Write first equation of motion.
Ans: v = u + at

Q6. Write second equation of motion.
Ans: x = ut + 1/2 at²

Q7. Write third equation of motion.
Ans: v² = u² + 2ax

Q8. What is average velocity in uniform acceleration?
Ans: (u + v)/2

Q9. What is acceleration when velocity is constant?
Ans: Zero

Q10. What is initial velocity for a body starting from rest?
Ans: Zero

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Short Answer Questions (2–3 Marks)

Q1. Why does area under velocity-time graph give displacement?
Ans: Velocity = displacement/time.
Area = velocity × time = m/s × s = m.
Hence, area under v–t graph gives displacement.

Q2. Differentiate between distance and displacement.
Ans: Distance is scalar and total path length.
Displacement is vector and shortest distance between initial and final position.

Q3. Define average velocity.
Ans: Average velocity = total displacement / total time.
For uniform acceleration, (u + v)/2.

Q4. What happens when acceleration is zero?
Ans: Velocity remains constant and motion becomes uniform motion.

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Derivations (3–5 Marks)

Q1. Derive first equation of motion.
Ans: a = (v - u)/t
v - u = at
v = u + at

Q2. Derive second equation of motion.
Ans: Displacement = area under v–t graph
x = ut + 1/2 (v - u)t
Using v - u = at,
x = ut + 1/2 at²

Q3. Derive third equation of motion.
Ans: v = u + at ⇒ t = (v - u)/a
x = (u + v)/2 × t
x = (u + v)(v - u)/2a
2ax = v² - u²
v² = u² + 2ax

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Numerical Question

Q1. A body starts from rest and accelerates at 4 m/s² for 5 s. Find final velocity.

Ans:
u = 0, a = 4 m/s², t = 5 s
v = u + at
v = 0 + 4 × 5 = 20 m/s

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MCQs

Q1. Slope of v–t graph gives:
Ans: Acceleration

Q2. Area under v–t graph gives:
Ans: Displacement

Q3. If acceleration is zero:
Ans: v = u

Q4. Which equation does not contain time?
Ans: v² = u² + 2ax

Q5. Unit of displacement is:
Ans: meter (m)

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Assertion and Reason

Q1.
Assertion: Area under v–t graph gives displacement.
Reason: Velocity × time gives displacement.
Ans: Both are true and Reason is correct explanation.

Q2.
Assertion: Slope of s–t graph gives acceleration.
Reason: Slope of s–t graph gives velocity.
Ans: Assertion false, Reason true.

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Fill in the Blanks

1. Slope of v–t graph gives ________.
Answer: acceleration

2. Area under v–t graph gives ________.
Answer: displacement

3. SI unit of velocity is ________.
Answer: m/s

4. A body at rest has initial velocity ________.
Answer: zero

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Match the Column

1. Slope of v–t graph → Acceleration
2. Area under v–t graph → Displacement
3. Slope of s–t graph → Velocity
4. Area under a–t graph → Change in velocity

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Case Study

Case: A car starts with velocity 10 m/s and accelerates at 2 m/s² for 5 s.

Q1. Final velocity?
v = 10 + 2×5 = 20 m/s

Q2. Displacement?
x = 10×5 + 1/2×2×25 = 75 m

Q3. Average velocity?
(u + v)/2 = (10 + 20)/2 = 15 m/s

Q4. Type of motion?
Uniformly accelerated motion

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Conclusion

This question bank covers MCQs, numericals, derivations, assertion-reason, fill in blanks, and case-based questions for CBSE Class 11 Physics exam preparation.

Kinematics Made Easy: All 3 Equations of Motion Explained for NEET & JEE 

Kinematic Equations of Motion with Velocity-Time Graph and Key Formulas Explained

🔗 Internal Links 

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Motion in a Straight Line Notes

Velocity-Time Graph Explanation

Derivation of v = u + at

Second Equation of Motion Proof

Third Equation of Motion Formula

NEET Physics Formula Sheet

Important Physics Graphs for NEET

Uniform Acceleration Problems

Class 11 Physics Chapter 3 Notes

Kinematics MCQs Practice Set