Dr Sanjay Kumar Pawar

Retardation (Negative Acceleration) Notes, MCQs & Numericals | CBSE & NEET

Educational infographic explaining Retardation (Negative Acceleration) with equations of motion, solved numericals, MCQs, and revision notes for CBSE Class 9 and NEET Physics.

Retardation (Negative Acceleration) explained with formulas, solved examples, and practice questions for CBSE Class 9 and NEET.

Retardation (Negative Acceleration) - Practice Questions

Retardation (Negative Acceleration)

CBSE | NCERT | NEET Foundation

Very Short Answer Questions (1 Mark)

What is retardation?
Retardation is the decrease in velocity of a moving body with time. It is also called negative acceleration.
What is another name for negative acceleration?
Deceleration or Retardation.
What is the SI unit of retardation?
m/s²
Can acceleration be negative?
Yes. Negative acceleration is called retardation.
A vehicle slows down. What is the sign of acceleration?
Negative (−)
What is the final velocity of a body that comes to rest?
0 m/s
Which equation of motion is used when time is not given?
v² = u² + 2as
What happens to the speed during retardation?
The speed decreases.
What is the SI unit of velocity?
m/s
What is the SI unit of displacement?
metre (m)

Short Answer Questions (2 Marks)

Q1. Differentiate between Acceleration and Retardation

Acceleration	Retardation
Speed increases	Speed decreases
Positive	Negative
Velocity increases	Velocity decreases

Q2. Write the three equations of motion.

v = u + at

s = ut + ½at²

v² = u² + 2as

Q3. Write the equations for retardation.

v = u − at

s = ut − ½at²

v² = u² − 2as

Solved Numerical Questions (3 Marks)

Question 1

A bike moves with an initial velocity of 20 m/s. It stops after 5 seconds. Find its retardation.

Given
u = 20 m/s
v = 0 m/s
t = 5 s

v = u + at

0 = 20 + 5a

5a = -20

a = -4 m/s²

Retardation = 4 m/s²

Question 2

A car moving at 30 m/s comes to rest in 6 seconds. Find the retardation.

Given
u = 30 m/s
v = 0 m/s
t = 6 s

v = u + at

0 = 30 + 6a

6a = -30

a = -5 m/s²

Retardation = 5 m/s²

Question 3

A train slows down from 40 m/s to 20 m/s in 10 seconds. Find the acceleration.

Given
u = 40 m/s
v = 20 m/s
t = 10 s

v = u + at

20 = 40 + 10a

10a = -20

a = -2 m/s²

Retardation = 2 m/s²

Question 4

A bus moving at 25 m/s stops after travelling 125 m. Find the retardation.

Given
u = 25 m/s
v = 0 m/s
s = 125 m

v² = u² + 2as

0 = 25² + 2 × a × 125

0 = 625 + 250a

250a = -625

a = -2.5 m/s²

Retardation = 2.5 m/s²

Question 5

A car moving at 15 m/s stops after travelling 45 m. Find the retardation.

Given
u = 15 m/s
v = 0 m/s
s = 45 m

v² = u² + 2as

0 = 15² + 2 × a × 45

0 = 225 + 90a

90a = -225

a = -2.5 m/s²

Retardation = 2.5 m/s²

Question 6

A scooter slows from 18 m/s to 6 m/s in 4 seconds. Find the retardation.

a = (6 − 18) / 4

a = -3 m/s²

Retardation = 3 m/s²

Question 7

A train moving at 72 m/s stops in 12 seconds. Find the retardation.

a = (0 − 72) / 12

a = -6 m/s²

Retardation = 6 m/s²

Question 8

A bus slows from 50 m/s to 20 m/s in 10 seconds. Find the retardation.

a = (20 − 50) / 10

a = -3 m/s²

Retardation = 3 m/s²

Question 9

A car moving at 10 m/s stops in 2 seconds. Find the retardation.

a = (0 − 10) / 2

a = -5 m/s²

Retardation = 5 m/s²

Question 10

A truck moving at 36 m/s comes to rest in 9 seconds. Find the retardation.

a = (0 − 36) / 9

a = -4 m/s²

Retardation = 4 m/s²

Multiple Choice Questions (MCQs)

1. Retardation is also called

A. Positive Acceleration
B. Uniform Motion
C. Negative Acceleration
D. Velocity

Answer: C. Negative Acceleration

2. SI unit of acceleration is

A. metre
B. second
C. m/s²
D. km/h

Answer: C. m/s²

3. When brakes are applied, acceleration becomes

A. Positive
B. Zero
C. Negative
D. Infinite

Answer: C. Negative

4. Which equation is used when time is not given?

A. v = u + at
B. s = ut
C. v² = u² + 2as
D. a = v/t

Answer: C. v² = u² + 2as

5. Final velocity of a body at rest is

A. 5 m/s
B. 10 m/s
C. 0 m/s
D. 100 m/s

Answer: C. 0 m/s

6. Retardation decreases

A. Time
B. Velocity
C. Distance
D. Mass

Answer: B. Velocity

7. Initial velocity is represented by

A. v
B. s
C. u
D. t

Answer: C. u

8. Final velocity is represented by

A. u
B. a
C. s
D. v

Answer: D. v

9. Time is represented by

A. a
B. t
C. s
D. u

Answer: B. t

10. Displacement is represented by

A. s
B. a
C. u
D. v

Answer: A. s

Higher Order Thinking Questions (HOTS)

Q1. Why is retardation called negative acceleration?

Retardation acts opposite to the direction of motion and decreases the velocity of a moving body. Therefore, its value is negative.

Q2. Can a body move forward while having negative acceleration?

Yes. If a moving body slows down while still moving forward, it has negative acceleration (retardation).

Assertion and Reason

Question 1

Assertion (A): Retardation decreases the speed of a moving body.

Reason (R): Retardation acts opposite to the direction of motion.

Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

Question 2

Assertion (A): A car moving at constant speed has retardation.

Reason (R): Constant speed means acceleration is zero.

Assertion is false, but Reason is true.

Case Study Question

A car is moving with an initial velocity of 60 m/s. The driver applies brakes and the car stops after travelling 180 m.

Questions

What is the initial velocity?
What is the final velocity?
Which equation of motion will be used?
Find the retardation.

Answers

Initial Velocity = 60 m/s

Final Velocity = 0 m/s

Formula Used:

v² = u² + 2as

0 = 60² + 2 × a × 180

0 = 3600 + 360a

360a = -3600

a = -10 m/s²

Retardation = 10 m/s²

Quick Revision

v = u + at

s = ut + ½at²

v² = u² + 2as

For Retardation

v = u − at

s = ut − ½at²

v² = u² − 2as

Exam Tips

Always write the SI unit in the final answer.
Write: Given → Formula → Substitution → Calculation → Final Answer.
Use v² = u² + 2as when time is not given.
Negative acceleration means retardation.
If the body stops, final velocity (v) = 0.

- Dr.Sanjaykumar Pawar

NCERT Class 11 Physics Chapter 1 Questions and Answers PDF

Student studying Class 11 Physics Units and Measurements chapter with SI units, measurements, formulas, and solved NCERT exercises.

Class 11 Physics Chapter 1 Units and Measurements with NCERT solutions and practice questions.

Class 11 Physics - Exercise 1.1 and 1.2

NCERT Class 11 Physics

Chapter 1: Units and Measurements

Exercise 1.1

Q1(a). The volume of a cube of side 1 cm is equal to ____ m³.

Answer:
Volume = (1 cm)³ = 1 cm³
1 cm = 10⁻² m
1 cm³ = (10⁻²)³ m³
= 10⁻⁶ m³

Final Answer: 1 × 10⁻⁶ m³

Q1(b). The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is equal to ____ (mm)².

Answer:
Surface Area = 2πr(r+h)
= 2 × 3.14 × 2.0 × (2.0 + 10.0)
= 150.72 cm²
1 cm² = 100 mm²
150.72 × 100 = 15072 mm²

Final Answer: 1.5 × 10⁴ mm²

Q1(c). A vehicle moving with a speed of 18 km h⁻¹ covers ____ m in 1 s.

Answer:
18 km h⁻¹ = 18 × (1000/3600)
= 5 m s⁻¹
Distance = Speed × Time
= 5 × 1
= 5 m

Final Answer: 5 m

Q1(d). The relative density of lead is 11.3. Its density is ____ g cm⁻³ or ____ kg m⁻³.

Answer:
Density = Relative Density × Density of Water
= 11.3 × 1
= 11.3 g cm⁻³

1 g cm⁻³ = 1000 kg m⁻³
11.3 × 1000 = 1.13 × 10⁴ kg m⁻³

Final Answer:
11.3 g cm⁻³
1.13 × 10⁴ kg m⁻³

Exercise 1.2

Q2(a). 1 kg m² s⁻² = ____ g cm² s⁻²

Answer:
1 kg = 10³ g
1 m² = 10⁴ cm²

1 kg m² s⁻²
= 10³ × 10⁴ g cm² s⁻²
= 10⁷ g cm² s⁻²

Final Answer: 10⁷ g cm² s⁻²

Q2(b). 1 m = ____ ly

Answer:
1 light year = 9.46 × 10¹⁵ m

1 m = 1 / (9.46 × 10¹⁵)
= 1.06 × 10⁻¹⁶ ly

Final Answer: 1.06 × 10⁻¹⁶ ly

Q2(c). 3.0 m s⁻² = ____ km h⁻²

Answer:
1 m = 10⁻³ km
1 s = 1/3600 h

3.0 × 10⁻³ × (3600)²
= 38880 km h⁻²

Final Answer: 3.9 × 10⁴ km h⁻²

Q2(d). G = 6.67 × 10⁻¹¹ N m² (kg)⁻² = ____ cm³ s⁻² g⁻¹

Answer:
1 N = kg m s⁻²

G = 6.67 × 10⁻¹¹ m³ kg⁻¹ s⁻²

1 m³ = 10⁶ cm³
1 kg⁻¹ = 10⁻³ g⁻¹

G = 6.67 × 10⁻¹¹ × 10⁶ × 10⁻³
= 6.67 × 10⁻⁸ cm³ s⁻² g⁻¹

Final Answer: 6.67 × 10⁻⁸ cm³ s⁻² g⁻¹

Class 11 Physics Practice Questions

Class 11 Physics - Units and Measurements

20 Practice Questions with Answers

Q1. A cube has a side of 2 cm. Find its volume.

Volume = a³
= 2³
= 8 cm³
Answer: 8 cm³

Q2. Convert 500 cm into metres.

500 ÷ 100 = 5 m
Answer: 5 m

Q3. Convert 1 km into metres.

1 km = 1000 m
Answer: 1000 m

Q4. Convert 72 km h⁻¹ into m s⁻¹.

72 × (1000/3600)
= 20 m s⁻¹
Answer: 20 m s⁻¹

Q5. A body moves with a speed of 15 m s⁻¹ for 4 s. Find the distance covered.

Distance = Speed × Time
= 15 × 4
= 60 m
Answer: 60 m

Q6. Convert 1 m² into cm².

1 m = 100 cm
1 m² = (100)² cm²
= 10000 cm²
Answer: 10000 cm²

Q7. Find the area of a square of side 5 m.

Area = side²
= 5²
= 25 m²
Answer: 25 m²

Q8. Convert 1 litre into cm³.

1 litre = 1000 cm³
Answer: 1000 cm³

Q9. A body has mass 200 g and volume 50 cm³. Find density.

Density = Mass / Volume
= 200 / 50
= 4 g cm⁻³
Answer: 4 g cm⁻³

Q10. What is the SI unit of force?

Answer: Newton (N)

Q11. What is the SI unit of energy?

Answer: Joule (J)

Q12. Convert 3 kg into grams.

3 × 1000 = 3000 g
Answer: 3000 g

Q13. Convert 2500 g into kilograms.

2500 ÷ 1000 = 2.5 kg
Answer: 2.5 kg

Q14. Find the total surface area of a cube of side 4 cm.

TSA = 6a²
= 6 × 4²
= 6 × 16
= 96 cm²
Answer: 96 cm²

Q15. What is the SI unit of time?

Answer: Second (s)

Q16. A cyclist covers 120 m in 20 s. Find speed.

Speed = Distance / Time
= 120 / 20
= 6 m s⁻¹
Answer: 6 m s⁻¹

Q17. Convert 36 km h⁻¹ into m s⁻¹.

36 × (1000 / 3600)
= 10 m s⁻¹
Answer: 10 m s⁻¹

Q18. What is the relative density of water?

Answer: 1

Q19. Find the volume of a cylinder of radius 3 cm and height 7 cm.

Volume = πr²h
= (22/7) × 3² × 7
= 198 cm³
Answer: 198 cm³

Q20. Express 1 day in seconds.

1 day = 24 × 60 × 60
= 86400 s
Answer: 86400 s

Quick Revision

SI unit of length = metre (m)
SI unit of mass = kilogram (kg)
SI unit of time = second (s)
SI unit of force = newton (N)
SI unit of energy = joule (J)
1 km = 1000 m
1 m = 100 cm
1 litre = 1000 cm³
Density = Mass / Volume
Speed = Distance / Time

Saturday, July 11, 2026