Understanding acceleration in physics is important because it explains how objects change their motion i.e., uniformly, non–uniformly.

Introduction

Imagine riding in a car, as it speeds up, the body feels a push against the seat, however, when it slows down, the body leans forward. This change in motion is what we call acceleration.

It is all around us, for instance, a sprinter racing across a track, a roller coaster zooming down a hill, or an apple falling from a tree. It is a fundamental part of physics that helps us describe how objects change their motion.

Here, we shall learn about what acceleration means, how it is calculated, and why it is so important.

What is Acceleration in Physics?

It is defined as,

“the rate of change of velocity of an object in a given frame of reference.”

Velocity refers to the speed of an object including the direction. So, acceleration mean speeding up, slowing down, or changing direction.

For example, if a car speeds up from 0 to 60 miles per hour and covers a certain displacement, it is accelerating. If the car slows down to stop, it is decelerating (meaning, decreasing acceleration or acceleration in the opposite direction).

Symbol

It is represented by the symbol a.

Type of Quantity

It is a derived physical quantity, as it depends upon two other physical quantities–velocity and time.

Unit

In International System of Units (SI), its unit is meter per squared second (m/s² or ms^-2).

Nature of Quantity

It is a vector quantity, means requires both magnitude and direction for its complete description. Also, it is in the direction of velocity if accelerating.

Mathematical Formulation

It is calculated using the formula,

a = Δv / Δt

a = (v_f – v_i) / Δt

Where,

• a is acceleration.
• Δv is the change in velocity (final velocity minus initial velocity).
• Δt is the change in time (how long it took for the change in velocity to happen).

Example

If a car speeds up from 0 to 20 m/s in 4 seconds, the acceleration would be,

a = (20 − 0) / 4 = 5 m/s²

This means the speed of the car is increasing by 5 meters per second every second.

Types of Acceleration

Uniform Acceleration

When velocity of an object changes equally in equal interval of time, its acceleration over time is constant and is called as uniform acceleration.

Example

For an object that is falling freely under the influence of gravity, accelerate at a steady rate (about 9.8 m/s²).

Non–Uniform Acceleration

When velocity of an object changes unequally in equal interval of time (or changes equally in unequal of time), its acceleration over time is variable and is called as non–uniform acceleration.

Example

A continuously speeding up vehicle while driving on a road experiences non-uniform acceleration. The similar case is when a vehicle slowing down or changing direction.

Average Acceleration

It is defined as,

“the total change in velocity of an object divided by the total time in a given frame of reference.”

It is the change in velocity over a certain period of time. This is useful for describing the overall rate of acceleration during a specific time interval, regardless of how the velocity may have varied within that time frame (i.e., uniformly or non–uniformly).

Mathematical Formulation

It is given by the formulas,

a_avg = Δv / Δt

a_avg = (v_f – v_i) / Δt

a_avg = (v_f² – v_i²) / 2d

Where,

• Δv = change in velocity
• Δt = time interval
• d = displacement covered

Example

If velocity of a car increases from 10 m/s to 30 m/s over 5 seconds, its average acceleration would be,

a_avg = (30 m/s − 10 m/s) / 5 sec =4 m/s²

Instantaneous Acceleration

It is defined as,

“the acceleration of an object at a specific moment in time in a given frame of reference.”

It is the rate of change of velocity at any given instant and is the limit of the average acceleration as the time interval approaches zero.

Mathematical Formulation

According to definition, it is given by the formula,

a_ins = lim_Δt→0 Δv / Δt

Where,

• a_ins = instantaneous acceleration
• Δv = change in velocity
• Δt = time interval

Example

When we press the accelerator in a car, the speed changes instantaneously. At that specific moment its acceleration is instantaneous.

Centripetal Acceleration

When an object moves in a circular path at a constant speed, its acceleration is called centripetal acceleration.

Although the speed remains constant, but the direction of object changes continuously, which means its velocity is changing. Also, this acceleration is directed towards the center of the circular path, and that is why, it is called as centripetal (meaning “center–seeking”) acceleration.

Mathematical Formulation

It calculated using the formula,

a_c = v² / r

Where,

• a_c​ = centripetal acceleration
• v = velocity of the object along the circular path
• r = radius of the circular path

Example
A satellite orbiting Earth or a car turning a corner (or moving on a circular track) experiences centripetal acceleration that is towards the center. It is because, even if they are moving at a constant speed, the direction changes continuously, which counts as acceleration.

Gravitational Acceleration

It is defined as,

“the acceleration experienced by an object due to the force of gravity.”

All objects, regardless of their mass, experience a constant gravitational acceleration in the absence of frictional effect.

Symbol

It is denoted by the symbol g.

Numerical Value

Near the surface of Earth its value is 9.8 m/s² (g = 9.8 m/s²).

Example

A feather or an apple, dropped from a height, accelerates towards the Earth at a constant rate of 9.8 m/s².

Common Misconceptions about Acceleration

Acceleration is not Just Speeding Up

People often think, only when we are moving faster, we will be accelerating. But acceleration also happens when we are slowing down. In this case it is called as deceleration, retardation, or negative acceleration. It also changes when we changing direction (like turning a corner).

Acceleration vs Velocity

Velocity includes both speed and direction, so a change in either (i.e., speed–magnitude, or direction) means acceleration. For example, going around a circle track at a constant speed is still acceleration because the direction is constantly changing.

Conclusion

In a nutshell, acceleration allows us to better understand how objects move and interact in our world. Whether it is a car picking up speed, an object falling to the ground, or a planet orbiting the sun, acceleration is a fundamental part of everyday life.

After knowing its types and how they are calculated, we can explain changes in motion with more clarity and precision. This knowledge not only deepens our understanding of physics but also gives us a tool to observe and analyse motion more effectively in the real world scenario.

Frequently Asked Questions (FAQs)

What is acceleration in physics and how is it different from velocity?

Acceleration refers to the rate of change of velocity, while velocity is the speed of an object in a given direction. Acceleration happens when there is a change in either speed or direction.

How do you calculate acceleration using velocity and time?

Acceleration is calculated by the formula,

a = Δv / Δt

Where,

• Δv = change in velocity
• Δt = time interval over which the change occurs.

What are the different types of acceleration in physics?

The main types include uniform acceleration, non-uniform acceleration, average acceleration, instantaneous acceleration, centripetal acceleration, and gravitational acceleration.

What is an example of uniform acceleration in real life?

A common example of uniform acceleration is an object in free fall, where the velocity increases at a constant rate due to gravity, around 9.8 m/s².

What is non-uniform acceleration and how does it differ from uniform acceleration?

Non-uniform acceleration occurs when velocity of an object changes at varying rates over time, unlike uniform acceleration, where the velocity changes at a constant rate.

What is centripetal acceleration and how is it calculated in circular motion?

Centripetal acceleration is the acceleration that occurs when an object moves in a circular path. It is calculated using the formula,

a_c = v² / r

Where,

• v = velocity along the circular path
• r = radius of the circle

What is gravitational acceleration and how does it affect objects on Earth?

Gravitational acceleration is the acceleration experienced by an object due to gravity of Earth, with a constant value of approximately 9.8 m/s² near the surface of the Earth.

What is the difference between acceleration and deceleration in physics?

Acceleration refers to an increase in velocity, while deceleration (negative acceleration) refers to a decrease in velocity. Both involve a change in the speed or direction of an object.

What is instantaneous acceleration and how is it measured?

Instantaneous acceleration is the acceleration of an object at a specific moment in time. It is measured as the limit of average acceleration as the time interval approaches zero.

Why acceleration is considered a vector quantity in physics?

Acceleration is a vector quantity because it has both magnitude (how much velocity changes) and direction (the direction of the velocity change), which is necessary for its complete description.