Acceleration and Retardation: Meaning, Formula, Difference for JKSSB Finance Accounts Assistant

Introduction

Acceleration and retardation are important concepts in the study of motion and frequently appear in competitive examinations such as JKSSB Finance Accounts Assistant, JKSSB Junior Assistant, SSC, Railway, and other government recruitment exams. These concepts help us understand how the velocity of an object changes with time.

When the velocity of an object increases, the object is said to be accelerating. Conversely, when its velocity decreases, the object experiences retardation or deceleration. Both acceleration and retardation describe the rate at which velocity changes and are measured in the same unit.

A clear understanding of acceleration and retardation is essential for solving numerical problems based on motion, velocity, and time. Questions may involve calculating acceleration, identifying the type of motion, or determining the retardation of a moving object. Therefore, aspirants should be familiar with the definitions, formulas, units, graphical representation, and practical applications of these concepts.

In this article, we will discuss the meaning of acceleration and retardation, their formulas, units, differences, solved numerical problems, important exam-oriented facts, and multiple-choice questions to help you prepare effectively for the JKSSB Finance Accounts Assistant examination.

What is Acceleration?

Acceleration is the rate of change of velocity of an object with respect to time. In simple words, when the velocity of an object increases or decreases over time, the object is said to be accelerating.

If a car increases its speed from 20 km/h to 40 km/h in a few seconds, its velocity changes and the car experiences acceleration. Similarly, a freely falling object accelerates towards the Earth due to the force of gravity.

Acceleration is a vector quantity, which means it has both magnitude and direction. The direction of acceleration depends on the direction in which the velocity changes.

Definition of Acceleration

Acceleration is defined as the change in velocity per unit time.

Mathematically,

Acceleration = Change in Velocity ÷ Time Taken

An object is said to have acceleration when:

• Its speed increases with time.
• Its speed decreases with time (retardation is a form of acceleration).
• The direction of motion changes.

SI Unit of Acceleration

The SI unit of acceleration is:

metre per second squared (m/s²)

This unit indicates how much the velocity changes every second.

Examples of Acceleration

• A car speeding up after a traffic signal turns green.
• A train gaining speed after leaving a station.
• A stone falling freely under gravity.
• A cyclist increasing speed while pedaling faster.

Key Points

• Acceleration is the rate of change of velocity.
• It is a vector quantity.
• SI unit: m/s²
• Acceleration can be positive, negative, or zero.
• If velocity remains constant, acceleration is zero.

Formula of Acceleration

Acceleration measures how quickly the velocity of an object changes with time. If an object gains speed, loses speed, or changes its direction of motion, it experiences acceleration. To determine the acceleration of an object, we use a simple mathematical formula that relates the change in velocity to the time taken.

Mathematical Formula of Acceleration

Acceleration = (Final Velocity − Initial Velocity) ÷ Time Taken

or

a = (v − u) / t

Where:

• a = Acceleration
• u = Initial Velocity
• v = Final Velocity
• t = Time Taken

Understanding the Formula

The term (v − u) represents the change in velocity of the object.

• Initial velocity (u) is the velocity of the object at the beginning of motion.
• Final velocity (v) is the velocity of the object after a certain period of time.
• Time (t) is the duration during which the change in velocity occurs.

When the change in velocity is divided by the time taken, we obtain the acceleration of the object.

For example, if a vehicle increases its velocity from 20 m/s to 40 m/s in 10 seconds, the change in velocity is 20 m/s. Dividing this by 10 seconds gives an acceleration of 2 m/s².

Conditions Based on the Formula

The value of acceleration can be positive, negative, or zero depending on the relationship between the initial and final velocities.

Positive Acceleration

When the final velocity is greater than the initial velocity, acceleration is positive.

Example:

• Initial velocity = 10 m/s
• Final velocity = 25 m/s

Since the velocity increases, the object has positive acceleration.

Negative Acceleration (Retardation)

When the final velocity is less than the initial velocity, acceleration becomes negative. This is known as retardation or deceleration.

Example:

• Initial velocity = 30 m/s
• Final velocity = 10 m/s

Since the velocity decreases, the object experiences retardation.

Zero Acceleration

When the initial velocity and final velocity are equal, there is no change in velocity and acceleration is zero.

Example:

• Initial velocity = 20 m/s
• Final velocity = 20 m/s

The object moves with constant velocity.

SI Unit of Acceleration

The SI unit of acceleration is metre per second squared (m/s²).

This unit can be derived from the formula:

Acceleration = Velocity / Time

= (m/s) / s

= m/s²

The unit m/s² indicates how much the velocity changes every second.

For example, an acceleration of 5 m/s² means that the velocity of the object increases by 5 metres per second every second.

Solved Example

A car increases its velocity from 10 m/s to 30 m/s in 5 seconds. Find its acceleration.

Given:

• Initial velocity (u) = 10 m/s
• Final velocity (v) = 30 m/s
• Time (t) = 5 s

Using the formula:

Acceleration = (v − u) / t

Acceleration = (30 − 10) / 5

Acceleration = 20 / 5

Acceleration = 4 m/s²

Answer: The acceleration of the car is 4 m/s².

Importance of the Acceleration Formula

The acceleration formula is widely used in physics and engineering to study the motion of objects. It helps in:

• Determining how quickly a vehicle gains speed.
• Calculating the motion of trains, cars, and aircraft.
• Studying the motion of falling bodies.
• Solving numerical problems in competitive examinations.

Important Points

• Acceleration is the rate of change of velocity with time.
• Formula: a = (v − u) / t
• SI unit: m/s²
• Positive acceleration indicates an increase in velocity.
• Negative acceleration indicates retardation or deceleration.
• Zero acceleration means constant velocity.
• Acceleration is a vector quantity because it has both magnitude and direction.

These points are frequently tested in JKSSB, SSC, Railway, and other government examinations.

Types of Acceleration

Acceleration is not always the same during the motion of an object. In some cases, the velocity changes by equal amounts in equal intervals of time, while in other cases the change in velocity is irregular. Based on the nature of the change in velocity, acceleration can be classified into two main types: Uniform Acceleration and Non-Uniform Acceleration.

Uniform Acceleration

An object is said to have uniform acceleration when its velocity changes by equal amounts in equal intervals of time.

In other words, the rate of change of velocity remains constant throughout the motion.

Definition

Uniform acceleration is the acceleration in which an object experiences the same change in velocity during every equal interval of time.

Example

Suppose a car increases its velocity as follows:

• After 1 second = 10 m/s
• After 2 seconds = 20 m/s
• After 3 seconds = 30 m/s
• After 4 seconds = 40 m/s

The velocity increases by 10 m/s every second. Since the change in velocity is constant, the car is moving with uniform acceleration.

Another common example is a freely falling object near the Earth’s surface. Due to gravity, the object accelerates uniformly at approximately 9.8 m/s².

Characteristics of Uniform Acceleration

• Change in velocity is equal in equal intervals of time.
• Acceleration remains constant.
• Velocity-time graph is a straight line.
• Easier to solve mathematically.

Non-Uniform Acceleration

An object is said to have non-uniform acceleration when its velocity changes by unequal amounts in equal intervals of time.

In this case, the rate of change of velocity is not constant.

Definition

Non-uniform acceleration is the acceleration in which the change in velocity varies during equal intervals of time.

Example

Consider a vehicle moving in heavy traffic:

• After 1 second = 10 m/s
• After 2 seconds = 18 m/s
• After 3 seconds = 22 m/s
• After 4 seconds = 35 m/s

The increase in velocity is not the same every second. Therefore, the vehicle is moving with non-uniform acceleration.

A car moving through city traffic, where the driver repeatedly accelerates and brakes, is a common example of non-uniform acceleration.

Characteristics of Non-Uniform Acceleration

• Change in velocity is unequal in equal intervals of time.
• Acceleration continuously changes.
• Velocity-time graph is a curved line.
• More common in real-life situations.

Difference Between Uniform and Non-Uniform Acceleration

Important Points

• Uniform acceleration means constant acceleration.
• Non-uniform acceleration means variable acceleration.
• A freely falling body exhibits uniform acceleration due to gravity.
• Most vehicles moving on roads experience non-uniform acceleration.
• In a velocity-time graph, a straight line indicates uniform acceleration, while a curved line indicates non-uniform acceleration.

What is Retardation (Negative Acceleration)?

Retardation, also known as deceleration or negative acceleration, is the rate at which the velocity of an object decreases with time. When a moving object slows down, it experiences retardation.

Just as acceleration increases the velocity of an object, retardation decreases its velocity. Therefore, retardation can be considered the opposite of acceleration.

Definition of Retardation

Retardation is defined as the decrease in velocity per unit time.

In simple words, if the velocity of an object becomes smaller as time passes, the object is said to be under retardation.

Why is Retardation Called Negative Acceleration?

Acceleration is calculated using the formula:

Acceleration = (Final Velocity − Initial Velocity) ÷ Time

When an object slows down, the final velocity becomes less than the initial velocity.

For example:

• Initial velocity = 30 m/s
• Final velocity = 10 m/s

Here,

(v − u) = (10 − 30) = −20

Since the value of acceleration is negative, it is called negative acceleration or retardation.

The negative sign does not mean the object is moving backward. It simply indicates that the velocity is decreasing.

Formula of Retardation

Retardation can be calculated using the same formula as acceleration:

Retardation = (Final Velocity − Initial Velocity) ÷ Time

or

a = (v − u) / t

Since the final velocity is less than the initial velocity, the result is negative.

In many numerical problems, only the magnitude of retardation is reported, and the negative sign is omitted.

SI Unit of Retardation

The SI unit of retardation is the same as that of acceleration:

metre per second squared (m/s²)

This unit indicates how much the velocity decreases every second.

For example, a retardation of 4 m/s² means that the velocity decreases by 4 m/s every second.

Examples of Retardation in Daily Life

Applying Brakes in a Car

When a driver applies the brakes, the speed of the car gradually decreases until it stops. This decrease in velocity is due to retardation.

Train Approaching a Station

As a train nears a station, the driver reduces its speed. The train experiences retardation until it comes to rest.

Ball Thrown Upward

When a ball is thrown vertically upward, its velocity decreases continuously due to the gravitational force acting downward. Hence, the ball experiences retardation during its upward journey.

Cyclist Slowing Down

A cyclist who stops pedaling gradually loses speed because of friction and air resistance. This is another example of retardation.

Solved Example

A bus moving at 25 m/s is brought to rest in 5 seconds. Find its retardation.

Given:

• Initial velocity (u) = 25 m/s
• Final velocity (v) = 0 m/s
• Time (t) = 5 s

Using the formula:

a = (v − u) / t

a = (0 − 25) / 5

a = −25 / 5

a = −5 m/s²

Therefore, the retardation of the bus is 5 m/s².

Characteristics of Retardation

• Velocity decreases with time.
• Acceleration has a negative value.
• The object gradually slows down.
• SI unit is m/s².
• Retardation acts opposite to the direction of motion.

Important Exam Points

• Retardation is also called deceleration or negative acceleration.
• It represents the rate of decrease of velocity.
• The SI unit of retardation is m/s².
• A negative value of acceleration indicates retardation.
• Applying brakes to a vehicle is the most common example of retardation.
• Retardation does not necessarily mean backward motion; it only indicates a reduction in velocity.

Questions based on the meaning, formula, and examples of retardation are commonly asked in JKSSB, SSC, Railway, and other competitive examinations.

Difference Between Acceleration and Retardation

Acceleration and retardation are two important concepts used to describe changes in the velocity of an object. While acceleration refers to an increase in velocity with time, retardation refers to a decrease in velocity with time. Understanding the difference between these concepts is essential for solving numerical and conceptual questions in competitive examinations.

Acceleration vs Retardation

Understanding Through an Example

Consider two cars:

Car A

A car increases its speed from 20 m/s to 40 m/s in 10 seconds.

• Initial velocity = 20 m/s
• Final velocity = 40 m/s

Since the velocity increases, the car experiences acceleration.

Car B

A car decreases its speed from 40 m/s to 20 m/s in 10 seconds.

• Initial velocity = 40 m/s
• Final velocity = 20 m/s

Since the velocity decreases, the car experiences retardation.

Graphical Difference

In a velocity-time graph:

• A line with a positive slope indicates acceleration.
• A line with a negative slope indicates retardation.

Thus, the slope of the velocity-time graph helps determine whether an object is accelerating or decelerating.

Similarities Between Acceleration and Retardation

Despite their differences, acceleration and retardation share some common features:

• Both describe the rate of change of velocity.
• Both are vector quantities.
• Both have the same SI unit, m/s².
• Both can be calculated using the formula:
  a = (v − u) / t
• Both are important for studying the motion of objects.

Important Points

• Acceleration increases velocity, whereas retardation decreases velocity.
• Positive acceleration indicates speeding up.
• Negative acceleration indicates slowing down.
• Both acceleration and retardation are measured in m/s².
• Applying brakes is a common example of retardation.
• A moving vehicle gaining speed is a common example of acceleration.

Questions asking the difference between acceleration and retardation are frequently asked in JKSSB, SSC, Railway, and other government examinations. Aspirants should be able to distinguish clearly between these two concepts and identify them in numerical problems.

Graphical Representation of Acceleration and Retardation

Graphs are useful tools for understanding the motion of an object. The graphical representation of acceleration and retardation helps us visualize how the velocity of an object changes with time.

The most commonly used graph for studying acceleration and retardation is the Velocity-Time (v-t) Graph. In this graph, time is represented on the horizontal (X) axis, while velocity is represented on the vertical (Y) axis.

Velocity-Time Graph and Acceleration

When the velocity of an object increases with time, the graph slopes upward from left to right. This indicates that the object is accelerating.

Positive Slope Indicates Acceleration

If the velocity increases uniformly with time, the velocity-time graph is a straight line with a positive slope.

Example:

In this case, the velocity increases by equal amounts in equal intervals of time. Therefore, the object has uniform acceleration.

Key Points

• Upward sloping line = Acceleration
• Positive slope = Positive acceleration
• Steeper slope = Greater acceleration

Velocity-Time Graph and Retardation

When the velocity of an object decreases with time, the graph slopes downward from left to right. This indicates retardation or negative acceleration.

Negative Slope Indicates Retardation

If the velocity decreases uniformly with time, the velocity-time graph is a straight line with a negative slope.

Example:

Here, the velocity decreases by equal amounts in equal intervals of time. Therefore, the object experiences uniform retardation.

Key Points

• Downward sloping line = Retardation
• Negative slope = Negative acceleration
• Steeper negative slope = Greater retardation

Zero Acceleration on a Velocity-Time Graph

When an object moves with constant velocity, its velocity does not change with time. In such a case, the velocity-time graph is a horizontal straight line.

Example:

Since the velocity remains constant, the acceleration is zero.

Key Points

• Horizontal line = Constant velocity
• Slope = Zero
• Acceleration = Zero

Relationship Between Slope and Acceleration

The slope (gradient) of a velocity-time graph gives the acceleration of the object.

Acceleration = Change in Velocity ÷ Time

Therefore:

• Positive slope → Positive acceleration
• Negative slope → Retardation
• Zero slope → Zero acceleration

Importance of Velocity-Time Graphs

Velocity-time graphs help us:

• Understand whether an object is speeding up or slowing down.
• Calculate acceleration and retardation easily.
• Compare different types of motion.
• Analyze motion visually without complex calculations.

Important Points

• The slope of a velocity-time graph represents acceleration.
• Positive slope indicates acceleration.
• Negative slope indicates retardation.
• Horizontal line indicates zero acceleration.
• A steeper slope means a greater rate of change of velocity.
• Questions based on velocity-time graphs are frequently asked in JKSSB, SSC, Railway, and other competitive examinations.

A clear understanding of velocity-time graphs helps aspirants solve both conceptual and numerical problems related to acceleration and retardation.

Relation Between Speed, Velocity and Acceleration

Speed, velocity, and acceleration are three fundamental concepts used to describe the motion of an object. These quantities are closely related because acceleration depends on changes in velocity, and velocity itself is related to speed and direction.

What is Speed?

Speed is the distance travelled by an object per unit time.

It tells us how fast an object is moving, regardless of its direction.

Formula:

Speed = Distance ÷ Time

Characteristics of Speed

• Speed is a scalar quantity.
• It has only magnitude and no direction.
• It is always positive or zero.
• SI unit of speed is metre per second (m/s).

Example

If a car travels 100 metres in 10 seconds, its speed is:

Speed = 100 ÷ 10 = 10 m/s

What is Velocity?

Velocity is the displacement of an object per unit time in a particular direction.

Unlike speed, velocity includes both magnitude and direction.

Formula:

Velocity = Displacement ÷ Time

Characteristics of Velocity

• Velocity is a vector quantity.
• It has both magnitude and direction.
• It can be positive, negative, or zero.
• SI unit of velocity is metre per second (m/s).

Example

If a person moves 50 metres east in 10 seconds, the velocity is:

Velocity = 50 ÷ 10 = 5 m/s east

What is Acceleration?

Acceleration is the rate of change of velocity with time.

Formula:

Acceleration = Change in Velocity ÷ Time

or

a = (v − u) / t

Where:

• u = Initial velocity
• v = Final velocity
• t = Time taken

Acceleration tells us how quickly the velocity changes.

Relationship Between Speed and Velocity

Speed and velocity are closely related but not identical.

• Speed considers only the magnitude of motion.
• Velocity considers both magnitude and direction.
• Speed can never be negative.
• Velocity can be positive or negative depending on direction.

For example, a car moving at 60 km/h north and another car moving at 60 km/h south have the same speed but different velocities.

Relationship Between Velocity and Acceleration

Acceleration depends directly on velocity.

If the velocity of an object changes, the object experiences acceleration.

The change may occur in:

Magnitude of Velocity

When the speed of an object increases or decreases.

Examples:

• A car speeding up.
• A train slowing down.

Direction of Velocity

Even if the speed remains constant, a change in direction causes acceleration.

Example:

• A car moving around a circular track at constant speed.
• The direction changes continuously, so the car is accelerating.

How Acceleration Affects Speed and Velocity

Positive Acceleration

When acceleration acts in the direction of motion, the velocity and speed increase.

Example:

A motorcycle accelerating on a straight road.

Negative Acceleration (Retardation)

When acceleration acts opposite to the direction of motion, the velocity and speed decrease.

Example:

A bus slowing down near a bus stop.

Zero Acceleration

When velocity remains constant, acceleration is zero.

Example:

A train moving at a constant speed on a straight track.

Real-Life Example

Consider a car moving at 20 m/s.

• If the driver presses the accelerator, the velocity increases to 30 m/s. The car experiences positive acceleration.
• If the driver applies brakes and the velocity decreases to 10 m/s, the car experiences retardation.
• If the car continues moving at 20 m/s without changing speed or direction, acceleration is zero.

Summary of the Relationship

Important Points

• Speed is a scalar quantity; velocity and acceleration are vector quantities.
• Speed depends on distance, whereas velocity depends on displacement.
• Acceleration depends on the change in velocity.
• A change in either speed or direction causes acceleration.
• Constant velocity means zero acceleration.
• SI units: Speed = m/s, Velocity = m/s, Acceleration = m/s².

Questions based on the relationship between speed, velocity, and acceleration are commonly asked in JKSSB, SSC, Railway, and other competitive examinations.

Numerical Problems on Acceleration

Numerical problems on acceleration are frequently asked in JKSSB, SSC, Railway, and other competitive examinations. Most questions are based on the standard acceleration formula:

Acceleration = (Final Velocity − Initial Velocity) ÷ Time Taken

or

a = (v − u) / t

To solve such problems, carefully identify the initial velocity, final velocity, and time, and then substitute the values into the formula.

Steps to Solve Acceleration Problems

1. Write the given values.
2. Identify:
   • Initial velocity (u)
   • Final velocity (v)
   • Time taken (t)
3. Apply the formula:
   a = (v − u) / t
4. Calculate the answer and write the correct unit (m/s²).

Problem 1

A car increases its velocity from 10 m/s to 30 m/s in 5 seconds. Find its acceleration.

Solution

Given:

• Initial velocity (u) = 10 m/s
• Final velocity (v) = 30 m/s
• Time (t) = 5 s

Using the formula:

a = (v − u) / t

a = (30 − 10) / 5

a = 20 / 5

a = 4 m/s²

Answer: The acceleration of the car is 4 m/s².

Problem 2

A train accelerates from 15 m/s to 45 m/s in 10 seconds. Calculate its acceleration.

Solution

Given:

• u = 15 m/s
• v = 45 m/s
• t = 10 s

Using the formula:

a = (45 − 15) / 10

a = 30 / 10

a = 3 m/s²

Answer: The acceleration of the train is 3 m/s².

Problem 3

A motorcycle starts from rest and reaches a velocity of 20 m/s in 4 seconds. Find its acceleration.

Solution

Given:

• Initial velocity (u) = 0 m/s
• Final velocity (v) = 20 m/s
• Time (t) = 4 s

Using the formula:

a = (20 − 0) / 4

a = 20 / 4

a = 5 m/s²

Answer: The acceleration of the motorcycle is 5 m/s².

Problem 4

An object moving at 8 m/s accelerates uniformly and reaches 32 m/s in 6 seconds. Calculate the acceleration.

Solution

Given:

• u = 8 m/s
• v = 32 m/s
• t = 6 s

Using the formula:

a = (32 − 8) / 6

a = 24 / 6

a = 4 m/s²

Answer: The acceleration of the object is 4 m/s².

Problem 5

A bus increases its velocity from 12 m/s to 24 m/s in 3 seconds. Find the acceleration.

Solution

Given:

• u = 12 m/s
• v = 24 m/s
• t = 3 s

Using the formula:

a = (24 − 12) / 3

a = 12 / 3

a = 4 m/s²

Answer: The acceleration of the bus is 4 m/s².

Numerical Problems on Retardation

Retardation, also known as negative acceleration or deceleration, occurs when the velocity of an object decreases with time. Numerical problems on retardation are commonly asked in JKSSB, SSC, Railway, and other competitive examinations.

The same formula used for acceleration is also used to calculate retardation:

a = (v − u) / t

Where:

• a = Acceleration or retardation (m/s²)
• u = Initial velocity (m/s)
• v = Final velocity (m/s)
• t = Time taken (s)

When the final velocity is less than the initial velocity, the value of acceleration becomes negative, indicating retardation.

Steps to Solve Retardation Problems

1. Write the given values.
2. Identify the initial velocity, final velocity, and time.
3. Apply the formula:
   a = (v − u) / t
4. If the answer is negative, the object is experiencing retardation.
5. Write the final answer with the unit m/s².

Problem 1

A car moving at 30 m/s is brought to rest in 6 seconds. Find its retardation.

Solution

Given:

• Initial velocity (u) = 30 m/s
• Final velocity (v) = 0 m/s
• Time (t) = 6 s

Using the formula:

a = (0 − 30) / 6

a = −30 / 6

a = −5 m/s²

Therefore, the retardation of the car is 5 m/s².

Problem 2

A train slows down from 40 m/s to 20 m/s in 10 seconds. Calculate its retardation.

Solution

Given:

• u = 40 m/s
• v = 20 m/s
• t = 10 s

Using the formula:

a = (20 − 40) / 10

a = −20 / 10

a = −2 m/s²

Therefore, the retardation of the train is 2 m/s².

Problem 3

A motorcycle moving at 25 m/s slows down to 10 m/s in 5 seconds. Find its retardation.

Solution

Given:

• u = 25 m/s
• v = 10 m/s
• t = 5 s

Using the formula:

a = (10 − 25) / 5

a = −15 / 5

a = −3 m/s²

Therefore, the retardation of the motorcycle is 3 m/s².

Problem 4

A bus moving at 18 m/s comes to rest in 3 seconds. Calculate its retardation.

Solution

Given:

• u = 18 m/s
• v = 0 m/s
• t = 3 s

Using the formula:

a = (0 − 18) / 3

a = −18 / 3

a = −6 m/s²

Therefore, the retardation of the bus is 6 m/s².

Problem 5

A cyclist reduces speed from 12 m/s to 4 m/s in 4 seconds. Find the retardation.

Solution

Given:

• u = 12 m/s
• v = 4 m/s
• t = 4 s

Using the formula:

a = (4 − 12) / 4

a = −8 / 4

a = −2 m/s²

Therefore, the retardation of the cyclist is 2 m/s².

Important Formulae at a Glance

In competitive examinations such as JKSSB Finance Accounts Assistant, SSC, Railway, and other government exams, direct questions are often asked from basic motion formulas. Therefore, aspirants should memorize the important formulas related to acceleration and retardation for quick revision and problem-solving.

This section provides all the essential formulas in one place.

1. Formula of Acceleration

Acceleration is the rate of change of velocity with time.

Acceleration = (Final Velocity − Initial Velocity) ÷ Time Taken

or

a = (v − u) / t

Where:

• a = Acceleration
• u = Initial velocity
• v = Final velocity
• t = Time taken

2. Formula of Retardation

Retardation is negative acceleration and is calculated using the same formula.

Retardation = (Final Velocity − Initial Velocity) ÷ Time Taken

or

a = (v − u) / t

When v < u, the value of acceleration becomes negative, indicating retardation.

3. Formula for Final Velocity

If acceleration, initial velocity, and time are known, the final velocity can be calculated as:

v = u + at

Where:

• v = Final velocity
• u = Initial velocity
• a = Acceleration
• t = Time

4. Formula for Initial Velocity

If final velocity, acceleration, and time are known:

u = v − at

5. Formula for Time

If acceleration and velocities are known:

t = (v − u) / a

6. Formula for Change in Velocity

Change in velocity is the difference between final and initial velocity.

Change in Velocity = Final Velocity − Initial Velocity

or

Δv = v − u

SI Units

Important Unit Conversions

Questions in competitive exams sometimes provide velocity in kilometres per hour (km/h). Such values should be converted into metres per second (m/s) before applying formulas.

Conversion from km/h to m/s

1 km/h = 5/18 m/s

To convert km/h into m/s:

Multiply by 5/18

Example:

72 km/h = 72 × 5/18 = 20 m/s

Conversion from m/s to km/h

1 m/s = 18/5 km/h

To convert m/s into km/h:

Multiply by 18/5

Example:

20 m/s = 20 × 18/5 = 72 km/h

Quick Formula Summary

Quick Facts

• Acceleration is the rate of change of velocity.
• Retardation is negative acceleration.
• SI unit of acceleration and retardation is m/s².
• Positive acceleration increases velocity.
• Negative acceleration decreases velocity.
• If velocity remains constant, acceleration is zero.
• Always convert km/h into m/s before solving numerical problems.
• Remember the conversion factors:
  • km/h to m/s → × 5/18
  • m/s to km/h → × 18/5

These formulas are frequently used in motion-related numerical problems and should be memorized thoroughly for quick and accurate problem-solving in JKSSB and other competitive examinations.

Frequently Asked Questions (FAQs)

1. What is acceleration?

Acceleration is the rate of change of velocity with respect to time. It describes how quickly the velocity of an object increases or decreases.

2. What is retardation?

Retardation, also known as deceleration or negative acceleration, is the rate at which the velocity of an object decreases with time.

3. What is the SI unit of acceleration?

The SI unit of acceleration is metre per second squared (m/s²).

4. Is acceleration a scalar or vector quantity?

Acceleration is a vector quantity because it has both magnitude and direction.

5. Can acceleration be negative?

Yes. When the velocity of an object decreases with time, acceleration becomes negative. This negative acceleration is called retardation or deceleration.

6. Can acceleration be zero?

Yes. If the velocity of an object remains constant and does not change with time, its acceleration is zero.

7. What is the formula for acceleration?

The formula for acceleration is:

a = (v − u) / t

Where:

• a = Acceleration
• u = Initial velocity
• v = Final velocity
• t = Time taken

8. What is the difference between speed and velocity?

Speed is the distance travelled per unit time and is a scalar quantity. Velocity is the displacement per unit time in a specific direction and is a vector quantity.

9. Why is retardation called negative acceleration?

Retardation is called negative acceleration because the final velocity is less than the initial velocity, making the value of acceleration negative.

10. What does an acceleration of 5 m/s² mean?

An acceleration of 5 m/s² means that the velocity of the object increases by 5 metres per second every second.

11. What is uniform acceleration?

Uniform acceleration occurs when the velocity changes by equal amounts in equal intervals of time.

12. What is non-uniform acceleration?

Non-uniform acceleration occurs when the velocity changes by unequal amounts in equal intervals of time.

13. Which graph is used to study acceleration?

The velocity-time graph is used to study acceleration. The slope of the graph gives the acceleration.

14. What does a negative slope in a velocity-time graph indicate?

A negative slope in a velocity-time graph indicates retardation or negative acceleration.

15. What is the acceleration due to gravity on Earth?

The acceleration due to gravity near the Earth’s surface is approximately 9.8 m/s².

16. Is a freely falling object accelerating?

Yes. A freely falling object accelerates uniformly due to the gravitational force acting on it.

17. What happens when a vehicle applies brakes?

When brakes are applied, the vehicle’s velocity decreases with time, resulting in retardation.

18. Why are acceleration and retardation important in competitive exams?

Acceleration and retardation are fundamental concepts of motion and are frequently asked in JKSSB, SSC, Railway, Defence, and other government examinations through theory-based and numerical questions.

Conclusion

Acceleration and retardation are fundamental concepts in the study of motion and play an important role in understanding how the velocity of an object changes with time. While acceleration refers to the increase in velocity per unit time, retardation refers to the decrease in velocity per unit time. Both concepts help explain the motion of vehicles, falling objects, moving trains, and many other real-life phenomena.

In this article, we discussed the meaning of acceleration and retardation, their formulas, SI units, types, graphical representation, relationship with speed and velocity, important numerical problems, exam-oriented one-liners, and multiple-choice questions. We also learned that acceleration can be positive, negative, or zero depending on how the velocity of an object changes.

For JKSSB Finance Accounts Assistant and other competitive examinations, aspirants should thoroughly understand the formula:

a = (v − u) / t

and be able to apply it in numerical problems. They should also remember that the SI unit of acceleration and retardation is m/s² and that the slope of a velocity-time graph represents acceleration.

Regular practice of numerical questions and MCQs will help strengthen conceptual understanding and improve problem-solving speed during examinations. By mastering the concepts covered in this chapter, candidates can confidently tackle questions related to motion, acceleration, and retardation in JKSSB, SSC, Railway, Defence, and other government recruitment exams.

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Rohit Thapa

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