# Formula of Kinetic Energy

Kinetic energy refers to a type of energy that an object or body possesses by virtue of its motion. It is possessed by every particle performing any kind of motion. Kinetic energy is a property of a moving body or object that does not depend on motion only, but it also depends upon the body's mass. Mechanical energy can be divided into two different types, the first one is Kinetic energy, and the second one is potential energy. Potential energy refers to a type of energy that an object or body possessed by virtue of its position. For example, when an object is a free fall, the object possesses kinetic energy. Kinetic energy can be due to rotation, translation, and vibration. We can calculate KE using the mass and velocity of that body.

In this article, we will discuss the formula to calculate the kinetic energy with certain examples.

## Method 1:

### Understanding Kinetic Energy

By knowing the Formula

The formula using for calculating the Kinetic energy is given below

KE = ½ mv2

Where

m = mass of an object or body.

v = velocity of an object or body.

Let's understand what is the mass and what is the velocity of an object.

Mass: Mass of an object or body refers to how much matter is in the object. It is denoted by m. Unit of mass is the joule.

Velocity: The velocity of an object refers to the rate at which the object changes its position. It is denoted by v. Unit of velocity is m/s.

Calculate the mass of an object:

When we solve a problem where the mass is not given, then first, you need to calculate the mass to proceed. This can be done by obtaining the mass in kg.

Find the velocity of an object:

You often face the problem while solving any problem, it does not give you the velocity of an object, but distance and time are given. Here, you need to calculate the velocity by applying the given formula.

Velocity = Distance/time = d/t

Example 1: If an object travels a distance of 8 meters in 2 sec, find the velocity of an object?

Solution:

Given,

Distance = 8 meter

Time = 2 sec

We know that,

V = distance/ time = 8/2 = 4 m/sec

Example 2: If an object travels a distance of 10 meters in 5 sec, find the velocity of an object?

Solution:

Given,

Distance = 10 meter

Time = 5 sec

We know that,

V = distance/ time = 10/5 = 2 m/sec

## Method 2

### Finding the Kinetic Energy

Write the equation:

The formula used to calculate the Kinetic energy is given below.

KE = ½ mv2

Where

m = mass of an object or body.

v = velocity of an object or body.

The value of KE should always be in joules J, which is the standard unit of measurement of KE.

Put the value of mass and velocity.

To calculate the KE, you need to put the value of mass and velocity in the formula. If the value of mass and velocity are not given in the questions, you need to calculate it.

Example 1:

Find the KE of an 80 kg men running with a velocity of 8 m/s.

Solution:

Given;

Mass = 80 kg

Velocity = 8 m/s

We know that,

KE = ½ mv2

KE = ½ × 80 × 82

= ½ × 80 × 64

= 40 × 64

= 256 J

Example 2:

Find the KE of a 120 kg man running with a velocity of 10 m/s.

Solution:

Given;

Mass = 120 kg

Velocity = 10 m/s

We know that,

KE = ½ mv2

KE = ½ × 120 × 102

= ½ × 120 × 100

= 60× 100

= 6000 J

Using KE calculate velocity or Mass

The formula using for calculating the Kinetic energy is given below

KE = ½ mv2

Where,

m = mass of an object or body

v = velocity of an object or body.

Put the Unknown Variables:

In some questions, you have the value of KE and mass. In that case, you need to calculate the value of the velocity.

Let's understand this concept with the help of an example

Example 1: What is the velocity of a body with a mass of 50 kg, and the value of kinetic energy is 2500 J?

Solution:

Given;

mass = 50 kg

Kinetic Energy = 2500 J

We know that

KE = ½ mv2

2500 = ½ × 50 × v2

v2 = 2500/25

v2 = 100

v = 10

Example 2: What is the velocity of a body with a mass of 60 kg and the value of kinetic energy is 480 J?

Solution:

Given;

mass = 60 kg

Kinetic Energy = 480 J

We know that

KE = ½ mv2

480 = ½ × 60 × v2

v2 = 480/30

v2 = 16

v = √16 = 4

Let's understand this concept with the help of an example

Suppose you have the value of KE and velocity. In that case, you need to find the value of the mass.

Example 1: Find the mass of an object with a kinetic energy of 500 J and a velocity of 10 m/s?

Solution:

Given;

Kinetic energy = 500 J

Velocity = 10 m/s

We know that

KE = ½ mv2

500 = ½ × m ×10 2

500 = ½ × m ×100

500 = 50 × m

m = 10 kg

Example 2: Find the mass of an object with a kinetic energy of 600 J and a velocity of 20 m/s?

Solution:

Given;

Kinetic energy = 600 J

Velocity = 20 m/s

We know that

KE = ½ mv2

600 = ½ × m ×20 2

500 = ½ × m ×400

500 = 200 × m

m = 2.5 kg

### Questions based on kinetic energy

Question 1: If a football has a mass of 3 kg, travels with a speed of 12 m/s, calculate the kinetic energy possessed by it.

Solution:

Given;

Mass = 3 kg

Velocity = 12 m/s

We know that,

Kinetic Energy = ½ mv2

KE = ½ ×3× (12)2

= ½ ×3× 144

= 216 J

Question 2: If a basketball has a mass of 4 kg, travels with a speed of 16 m/s, calculate the kinetic energy possessed by it.

Solution:

Given;

Mass = 4 kg

Velocity = 16 m/s

We know that,

Kinetic Energy = ½ mv2

KE = ½ ×4× (16)2

= ½ ×4× 256

= 512 J

Question 3: If a 12 kg object was traveling at a speed of 120 m/s. Now, this mass transfers all its energy to a mass of 24 k. What will be the velocity of the 24 kg mass after being hit by it?

Solution:

We know that,

KE = ½ mv2

First, we will calculate the KE of the heavier object

Given,

M = 12 kg and v = 120 m/s

We know that,

KE = ½ mv2

= ½ × 12 × (120)2

= ½ × 12 × 14400

= 86400 J

Now, this energy is transferred to another ball

Given;

Mass = 24 Kg

Velocity =?

We have calculated the value of kinetic energy

KE = 86400

So,

We know that,

KE = ½ mv2

86400 = ½ (24) v2

v2 = 86400/12 = 7200

v = 60 m/s

Question 4: If an 8 kg object was traveling at a speed of 80 m/s. Now, this mass transfers all its energy to a mass of 16 k. What will be the velocity of the 16 kg mass after being hit by it?

Solution:

We know that,

KE = ½ mv2

First, we will calculate the KE of the heavier object

Given,

M = 8 kg and v = 80 m/s

We know that,

KE = ½ mv2

= ½ × 8 × (80)2

= ½ × 8 × 6400

= 25600 J

Now, this energy is transferred to another ball

Given;

Mass = 16 Kg

Velocity =?

We have calculated the value of kinetic energy

KE = 25600

So,

We know that,

KE = ½ mv2

25600 = ½ (16) v2

v2 = 25600/16 = 16

v = 4 m/s

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