# Understanding acceleration

Acceleration in our daily conversation means to speed up. It can occur in different applications be it transportation, human, animal, object, equipment, etc. a change in velocity of an object is known as acceleration. This is why the greater the acceleration, the greater the change in velocity over a given time Today you’ll get to know the definition, examples, formula, unit, types, calculations, and difference between acceleration and velocity. You’ll also learn the velocity-time graph

Read more: The Three Newton’s laws of motion

Contents

## What is acceleration?

Acceleration refers to the rate of change of velocity with time or the rate at which velocity inter-changes with time. It occurs in terms of both speed and direction. when a point or an object is moving in a straight line is accelerated if it speeds up or slows down. Motion on a circle is accelerated even if the speed is constant. Therefore, the direction is continually changing, this effect also contributes to the acceleration for all other kinds of motion.

Since acceleration has both a magnitude and direction, it’s a vector quantity. With this, acceleration can be defined as the change in the velocity vector in a time interval, divided by the time interval. Instantaneous acceleration which is known as a precise movement and location is determined by the limit of the ratio of the change in velocity during a given time interval to the time interval is the time interval goes to zero.

For instance, if velocity is expressed in meters per second, the acceleration will be expressed in meters per square second.

The confusing part about acceleration and velocity is that they are not the same thing. Most people think if an object has a large velocity, then the acceleration will also be large. Also, think of the object’s velocity is small then the acceleration is small. But this is not true. The value of the velocity at a given moment does not determine the acceleration. That is, one can be changing its velocity at a high rate regardless of moving slow or fast.

Read more: Understanding distance and displacement

## Formula and Unit for acceleration

The formula for acceleration is given as:

Acceleration is equal to final velocity minus initial velocity all over time.

Acceleration is then equal to a change in velocity all over time. This can be mathematically expressed as:  You can use the acceleration equation to calculate acceleration. Here is the most common acceleration formula:

a=

 Δv Δt

where Δv is the change in velocity and Δt is the change in time.

You can also write the acceleration equation like this:

a=

 v(f)−v(i) t(f)−t(i)

In this acceleration equation, v(f) is the final velocity while is v(i) initial velocity. T(f) is the final time and t(i) is the initial time.

Read more: How Force changes the State of Motion

where:

a is the acceleration in m.s-2

Vf is the final velocity in m.s-1

t is the time interval in s and

is the small change in the velocity in m.s-1

So, the SI unit of acceleration can be given as meter per second m/s2

## Examples

Below is the common form of acceleration that occurs in our daily life.

• A boy running at a different speed
• The movement of Bee in a different direction
• Someone walking
• A moving vehicle
• Moving a cart in a glossary store
• A movement of an arrow
• A kicked ball
• Some flying birds
• The movement of a shark at a uniform velocity.

Read more: Relationship between Force and Motion

## Types of acceleration

The different types of acceleration are uniform and non-uniform acceleration and average acceleration.

### Uniform and non-uniform acceleration:

In a situation where speed remains constant but the body is accelerated, it is possible in circular where the speed remains constant but since the direction is changing hence the velocity changes. With this, the body is said to be accelerated.

### Average acceleration:

This type of acceleration over some time is defined as the total change in velocity in the given interval divided by the time taken for the change. For a given interval of time, it can be denoted as  . mathematically,

Read more: How Force changes the State of Motion

## Calculations

Let take some examples to see what acceleration looks like.

#### Example 1

A bald eagle is flying to the left with a speed of 34meters per second when a gust of wind blows back against the eagle causing it to slow down with a consent acceleration of a magnitude 8 meters per second squared. What will be the speed of the bald eagle be after the wind has blown for 3 seconds?

From our equation

we make Vf the subject of the formula

Vf = Vi + at

Vf = -34 m/s + 8 m/s2

Vf = -34m/s + 8m/s2 (3s)

Vf = -10m/s

So, the final speed is = +10m/s

#### Example 2

Suppose a car moves from a velocity of 20m/s to its final velocity of 30m/s in 5seconds, calculate it average acceleration.

Using a = v – ­u/t

V = 30m/s

U = 20m/s

T = 5seconds

a = 30 – 20/5

­ a = 10/5

a = 2m/s2

Acceleration is a vector quantity and a vector quantity has both magnitude and direction. if an object is changing its velocity, it shows that such an object is accelerating. For example, a bicycle increases with a speed of 2m/s, and a car moves with an increasing speed of 5m/s.

#### Example 3

A neurotic tiger shark starts from rest and speeds up uniformly to 12meters per second in a time of 3 seconds. What was the magnitude of the average acceleration of the tiger shark?

a = 4m/s2

#### Example 4

What will be the acceleration of an object which moves with uniform velocity?