NCERT Class 11 Physics Chapter 2 Exercise 2.8 to 2.14 Solutions (CBSE 2026)

-  Dr.Sanjaykumar Pawar  

 

Internal Links

1. NCERT Class 11 Physics Chapter 2 Motion in a Straight Line Notes

2. NCERT Class 11 Physics Exercise 2.1 to 2.7 Solutions

3. NCERT Class 11 Physics Chapter 3 Motion in a Plane Solutions

4. Important Class 11 Physics Formulas PDF

5. CBSE Class 11 Physics Previous Year Questions

6. Motion in a Straight Line MCQs with Answers

7. Speed, Velocity and Acceleration Notes

8. Class 11 Physics Revision Notes

9. NCERT Exemplar Class 11 Physics Solutions

10. Complete Class 11 Physics Study Material

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NCERT Solutions Class 11 Physics

Chapter 2: Motion in a Straight Line

Exercise 2.8 to 2.14

Question 2.8

A ball is dropped from a height of 90 m on a floor. At each collision with the floor, the ball loses one tenth of its speed. Plot the speed-time graph of its motion between t = 0 to 12 s.

Given:

• Height = 90 m
• g = 9.8 m/s²
• Loss of speed after every collision = 10%

Step 1: Time taken to reach the floor

h = ½gt²

90 = ½ × 9.8 × t²

t² = 180/9.8

t = 4.29 s

Step 2: Speed just before collision

v = gt

v = 9.8 × 4.29

v = 42 m/s

Step 3: Speed after collision

v' = 0.9 × 42

v' = 37.8 m/s

Step 4: Time taken to move upward

t = v'/g

t = 37.8/9.8

t = 3.86 s

Graph Description:

• Speed increases uniformly from 0 to 42 m/s during first 4.29 s.
• At collision speed suddenly decreases to 37.8 m/s.
• Speed decreases linearly to zero while moving upward.
• Then increases again while falling downward.

Speed-Time graph consists of straight line segments with sudden vertical drops at collisions.

Question 2.9

Explain clearly, with examples, the distinction between: (a) Magnitude of displacement and total path length (b) Magnitude of average velocity and average speed.

(a) Magnitude of Displacement and Total Path Length

Magnitude of Displacement	Total Path Length
Shortest distance between initial and final positions.	Actual distance travelled.
Depends only on initial and final positions.	Depends on actual path followed.
Always less than or equal to path length.	Always greater than or equal to displacement.

Example:

Particle moves 3 m east and 4 m north. Displacement = √(3² + 4²) = 5 m Path Length = 3 + 4 = 7 m

(b) Magnitude of Average Velocity and Average Speed

Average Velocity = Displacement / Time

Average Speed = Total Path Length / Time

Since total path length ≥ displacement,

Average Speed ≥ Magnitude of Average Velocity

Equality occurs only when motion is along a straight line without changing direction.

Question 2.10

A man walks on a straight road from his home to a market 2.5 km away with a speed of 5 km h⁻¹. Finding the market closed, he instantly turns and walks back home with a speed of 7.5 km h⁻¹. Find: (a) Magnitude of average velocity (b) Average speed

(a) Magnitude of Average Velocity

Net displacement = 0 Average Velocity = 0 / Total Time = 0

Magnitude of Average Velocity = 0 km h⁻¹

(b) Average Speed

Time to market = 2.5/5 = 0.5 h

Time to return = 2.5/7.5 = 0.333 h

Total distance = 5 km Total time = 0.5 + 0.333 = 0.833 h

Average Speed = 5 / 0.833 = 6 km h⁻¹

Average Speed = 6 km h⁻¹

Question 2.11

Why is there no distinction between instantaneous speed and magnitude of instantaneous velocity?

Instantaneous Speed = Magnitude of Instantaneous Velocity

Velocity has both magnitude and direction, whereas speed is only magnitude. At any instant, speed is simply the magnitude of velocity.

Instantaneous Speed = |Instantaneous Velocity|

Question 2.12

Look at the graphs (a) to (d) carefully and state which of these cannot represent one-dimensional motion of a particle.

• Graph (a): Impossible because one instant corresponds to more than one position.
• Graph (b): Impossible because one instant corresponds to more than one velocity.
• Graph (c): Impossible because speed cannot be negative.
• Graph (d): Impossible because total path length can never decrease.

All graphs (a), (b), (c) and (d) cannot represent one-dimensional motion.

Question 2.13

Figure 2.11 shows the x-t plot of one-dimensional motion of a particle. Is it correct to say from the graph that the particle moves in a straight line for t < 0 and on a parabolic path for t > 0?

No. The graph is an x-t graph and not the actual trajectory of the particle.

For t < 0, x remains constant, showing that the particle is at rest.

For t > 0, x increases with time and velocity increases continuously.

The graph represents variation of position with time and not the actual path of motion.

Question 2.14

A policeman moving at 30 km h⁻¹ fires a bullet at a thief's car speeding away in the same direction with a speed of 192 km h⁻¹. If the muzzle speed of the bullet is 150 m s⁻¹, with what speed does the bullet hit the thief's car?

Step 1: Convert speeds into m/s

Policeman = 30 × 5/18 = 8.33 m/s

Thief = 192 × 5/18 = 53.33 m/s

Step 2: Bullet speed relative to ground

Bullet speed = 150 + 8.33 = 158.33 m/s

Step 3: Relative speed of bullet with respect to thief

158.33 − 53.33 = 105 m/s

Speed of bullet relative to thief's car = 105 m/s

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Velocity Class 11 Notes, MCQs, Questions Answers for CBSE & NEET

 VELOCITY

│

├── Definition

│   ├── Rate of change of displacement

│   ├── Vector quantity

│   ├── Has magnitude + direction

│   └── SI Unit = m/s

│

├── Average Velocity

│   │

│   ├── Formula

│   │   └── v = Δr / Δt

│   │

│   ├── Component Form

│   │   ├── v = (Δx/Δt)i + (Δy/Δt)j

│   │   ├── i → x-axis unit vector

│   │   └── j → y-axis unit vector

│   │

│   ├── Direction

│   │   └── Same as displacement

│   │

│   └── Depends On

│       ├── Initial position

│       └── Final position

│

├── Instantaneous Velocity

│   │

│   ├── Meaning

│   │   └── Velocity at a particular instant

│   │

│   ├── Formula

│   │   ├── v = lim(Δt→0) (Δr/Δt)

│   │   └── v = dr/dt

│   │

│   ├── Important Concept

│   │   ├── Δt → 0

│   │   ├── Δr → very small

│   │   └── Direction becomes tangent

│   │

│   └── Direction

│       └── Tangential to path

│

├── Component Form of Velocity

│   │

│   ├── Position Vector

│   │   └── r = xi + yj

│   │

│   ├── Velocity Vector

│   │   └── v = (dx/dt)i + (dy/dt)j

│   │

│   ├── x-component

│   │   └── vx = dx/dt

│   │

│   └── y-component

│       └── vy = dy/dt

│

├── Magnitude of Velocity

│   │

│   ├── Formula

│   │   └── v = √(vx² + vy²)

│   │

│   └── Based On

│       └── Pythagoras theorem

│

├── Direction of Velocity

│   │

│   ├── tanθ = vy/vx

│   │

│   └── θ = tan⁻¹(vy/vx)

│

├── Important NEET Points

│   ├── Velocity is vector quantity

│   ├── Average velocity = displacement/time

│   ├── Instantaneous velocity = derivative of displacement

│   ├── Direction is tangent to path

│   ├── vx = dx/dt

│   ├── vy = dy/dt

│   └── v = √(vx² + vy²)

│

└── Example

    │

    ├── Given

    │   ├── vx = 3 m/s

    │   └── vy = 4 m/s

    │

    ├── Magnitude

    │   └── v = 5 m/s

    │

    └── Direction

        └── θ ≈ 53° 

Easy Velocity Notes with MCQs and CBSE Class 11 Physics Questions for NEET Preparation 

- Dr.Sanjaykumar pawar

Internal Links

Motion in a Straight Line Notes

Scalars and Vectors Class 11

Distance and Displacement Notes

Speed and Velocity Difference

Acceleration Notes Class 11

Projectile Motion Notes

Kinematics Formula Sheet

NEET Physics Important Questions

CBSE Class 11 Physics MCQs

Units and Dimensions Notes

Velocity Notes for NEET Beginners

1. Meaning of Velocity

Velocity tells us how fast an object moves and in which direction it moves.

• Velocity is a vector quantity.
• It has both magnitude and direction.
• SI unit of velocity is m/s.

Example: A car moving at 20 m/s towards east has velocity.

2. Average Velocity

Average velocity is defined as the ratio of displacement to total time interval.

v = Δr / Δt

Where:

• Δr = displacement
• Δt = time interval

v = (Δx/Δt) i + (Δy/Δt) j

Here:

• i = unit vector along x-axis
• j = unit vector along y-axis

3. Direction of Average Velocity

The direction of average velocity is always same as the direction of displacement.

Average velocity depends only on initial and final positions.

4. Instantaneous Velocity

Instantaneous velocity means velocity at a particular instant of time.

It is obtained when the time interval becomes extremely small.

v = lim (Δt → 0) (Δr / Δt)

v = dr / dt

5. Direction of Instantaneous Velocity

As Δt approaches zero:

• Displacement becomes very small.
• The displacement direction becomes tangent to the path.

Therefore, instantaneous velocity is always tangential to the path.

6. Component Form of Velocity

If position vector is:

r = xi + yj

Then velocity becomes:

v = (dx/dt)i + (dy/dt)j

7. Velocity Components

vx = dx/dt

vy = dy/dt

• vx = velocity along x-axis
• vy = velocity along y-axis

8. Magnitude of Velocity

The magnitude of velocity is:

v = √(vx² + vy²)

This formula is based on Pythagoras theorem.

9. Direction of Velocity Vector

The direction of velocity is given by angle θ.

tanθ = vy / vx

θ = tan⁻¹(vy/vx)

10. Important NEET Points

• Velocity is a vector quantity.
• Average velocity = displacement / time.
• Instantaneous velocity = derivative of displacement.
• Velocity is tangential to the path.
• vx = dx/dt
• vy = dy/dt
• Magnitude = √(vx² + vy²)
• Direction = tan⁻¹(vy/vx)

11. Quick Revision Table

Quantity	Formula
Average Velocity	Δr / Δt
Instantaneous Velocity	dr / dt
x-component	dx / dt
y-component	dy / dt
Magnitude	√(vx² + vy²)
Direction	tanθ = vy / vx

12. Simple Example

Given:

• vx = 3 m/s
• vy = 4 m/s

Magnitude:

v = √(3² + 4²)

v = 5 m/s

Direction:

θ = tan⁻¹(4/3)

θ ≈ 53°

Therefore, velocity = 5 m/s at 53° to x-axis.

NEET Physics Notes - Velocity Chapter

CBSE Class 11 Physics - Velocity Questions & Answers

1. Multiple Choice Questions (MCQs)

Q1. Velocity is a:

• A) Scalar quantity
• B) Vector quantity
• C) Tensor quantity
• D) Dimensionless quantity

Answer: B) Vector quantity

Q2. Average velocity is equal to:

• A) Distance / Time
• B) Speed / Time
• C) Displacement / Time
• D) Acceleration / Time

Answer: C) Displacement / Time

Q3. SI unit of velocity is:

• A) m
• B) m/s
• C) m/s²
• D) km/h

Answer: B) m/s

Q4. The direction of instantaneous velocity is:

• A) Perpendicular to path
• B) Tangential to path
• C) Opposite to motion
• D) Random

Answer: B) Tangential to path

2. Very Short Answer Questions

Q1. Define velocity.

Velocity is the rate of change of displacement with time.

Q2. Write SI unit of velocity.

SI unit of velocity is metre per second (m/s).

Q3. What is instantaneous velocity?

Velocity at a particular instant of time is called instantaneous velocity.

3. Short Answer Questions

Q1. Differentiate between speed and velocity.

Speed	Velocity
Scalar quantity	Vector quantity
Distance/time	Displacement/time
No direction	Has direction

Q2. Define average velocity with formula.

Average velocity is displacement divided by total time taken.

v = Δr / Δt

4. Long Answer Questions

Q1. Explain average velocity and instantaneous velocity.

Average Velocity

Average velocity is the ratio of displacement to total time interval.

v = Δr / Δt

• It is a vector quantity.
• Direction is same as displacement.

Instantaneous Velocity

Velocity at a particular instant is called instantaneous velocity.

v = lim (Δt → 0) (Δr / Δt)

Its direction is tangential to the path.

Q2. Derive magnitude of velocity using components.

If velocity components are vx and vy:

v = √(vx² + vy²)

This formula is obtained using Pythagoras theorem.

tanθ = vy / vx

5. Assertion and Reason Questions

Q1.

Assertion (A): Velocity is a vector quantity.

Reason (R): Velocity has magnitude as well as direction.

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

Q2.

Assertion (A): Average velocity can be zero.

Reason (R): Displacement can be zero.

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

6. Fill in the Blanks

1. Velocity is a __________ quantity.
2. SI unit of velocity is __________.
3. Average velocity is displacement divided by __________.
4. Instantaneous velocity acts along the __________ to the path.
5. Velocity along x-axis is represented by __________.

1. Vector
2. m/s
3. Time
4. Tangent
5. vx

7. Statement Based Questions

Q1.

Statement 1: Velocity depends on displacement.

Statement 2: Speed depends on distance.

Answer: Both statements are true.

Q2.

Statement 1: Velocity can be negative.

Statement 2: Speed can be negative.

Answer: Statement 1 is true but Statement 2 is false.

8. Match the Columns

Column A	Column B
1. Velocity	a. Scalar quantity
2. Speed	b. Tangential direction
3. Instantaneous velocity	c. Vector quantity
4. Average velocity	d. Displacement/time

Answers:

• 1 → c
• 2 → a
• 3 → b
• 4 → d

9. Case Study Questions

A particle moves along a curved path. At point P, its velocity components are:

• vx = 6 m/s
• vy = 8 m/s

Q1. Find magnitude of velocity.

v = √(6² + 8²)

v = 10 m/s

Q2. Find direction of velocity.

tanθ = 8/6

θ ≈ 53°

Q3. What is direction of instantaneous velocity?

Tangential to the path.

10. Numerical Questions

Q1. A body moves 20 m east in 4 s. Find average velocity.

v = 20 / 4

Average velocity = 5 m/s east

Q2. If vx = 5 m/s and vy = 12 m/s, find resultant velocity.

v = √(5² + 12²)

v = 13 m/s

11. HOTS Questions

Q1. Can average speed be greater than average velocity?

Yes. Distance is always greater than or equal to displacement.

Q2. Can velocity change even if speed remains constant?

Yes. In circular motion direction changes continuously, so velocity changes.

CBSE Class 11 Physics - Velocity Chapter Questions Answers