Understanding Acceleration: Meaning, Units and Real-Life Applications

Introduction

Motion is all around us. Even when something looks still, it is usually moving in some way. The Earth itself moves around the Sun, and everything on it moves along too. On a daily basis, we clearly see motion in cars, trains, airplanes, and even a ceiling fan spinning to circulate air. To understand motion properly, we rely on two key ideas: velocity and acceleration. In this article, we’ll focus on acceleration and break it down in a simple, student-friendly way.

What is Acceleration?

Acceleration tells us how fast the velocity of an object changes with time. Since velocity includes both speed and direction, any change in either of these leads to acceleration. This makes acceleration a vector quantity.

For example, if an object’s velocity changes from u to v:

• If v is greater than u, the object speeds up and the acceleration is positive.

• If v is smaller than u, the object slows down. This is called deceleration or negative acceleration.

• If the velocity stays the same, the acceleration is zero.

When velocity changes by the same amount every second, the motion is said to have uniform acceleration. If the change is irregular, the acceleration is non-uniform.

Unit and Dimensional Formula of Acceleration

The SI unit of acceleration is metres per second squared (m/s²). This comes directly from the formula, since acceleration is velocity divided by time.

Other commonly used units include km/h².

The dimensional formula of acceleration is:
[M⁰ L T⁻²]

Other Units of Acceleration

SI Unit of Acceleration

In the SI system, acceleration is measured in m/s². This means that if an object’s velocity changes by 1 m/s every second, its acceleration is 1 m/s².

This can be derived using:

• SI unit of velocity: m/s

• SI unit of time: s

Feet per Second Squared

In the foot-pound-second system, acceleration is measured in ft/s². If a body’s velocity changes by 1 foot per second in 1 second, its acceleration is 1 ft/s².

Gal (Galileo) Unit

The Gal is named after Galileo Galilei, who studied gravity in detail.
1 gal = 0.01 m/s².

Standard Gravity

Standard gravity refers to the average acceleration caused by Earth’s gravitational pull. Its value is approximately 9.8 m/s². This value can vary slightly depending on altitude and location, but it does not depend on the mass of the object.

Planck Acceleration

Planck acceleration is a theoretical concept defined using fundamental constants. It represents the change in velocity from rest to the speed of light over Planck time.

Types of Acceleration

1. Average Acceleration

Average acceleration is calculated over a time interval. It is found by dividing the change in velocity by the total time taken.

2. Instantaneous Acceleration

Instantaneous acceleration is the acceleration at a specific moment in time. It is obtained by taking the limit of average acceleration as the time interval becomes very small.

3. Centripetal Acceleration

An object moving in a circle experiences acceleration even if its speed stays constant. This is because the direction of velocity keeps changing.

The acceleration that pulls the object toward the centre of the circular path is called centripetal acceleration.

4. Gravitational Acceleration

Gravitational acceleration is the acceleration experienced by an object due to gravity. On Earth, its average value is 9.8 m/s². In the absence of air resistance, all objects fall at the same rate, regardless of their mass.

Solved Examples

Example 1:
A car’s velocity increases from 10 m/s to 50 m/s in 10 seconds.
Acceleration = (50 − 10) / 10 = 4 m/s²

Example 2:
A car of mass 900 kg moves in a circle of radius 25 m at a constant speed of 10 m/s.
Centripetal acceleration = v² / r = 100 / 25 = 4 m/s², acting toward the centre of the circle.

Summary

Acceleration measures how quickly velocity changes with time. It is a vector quantity, meaning it has both magnitude and direction. Motion can be accelerated even when speed is constant, as long as the direction changes, such as in circular motion. One of the most familiar forms of acceleration is gravitational acceleration, which on Earth has an average value of 9.8 m/s².

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