# Kinetic Energy

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## Introduction

The kinetic energy of an object is defined as the energy it possesses by virtue of its motion. Some of the common activities in life such as walking, jumping, throwing, falling, etc. involve kinetic energy. When work is done on an object, energy is transferred, and finally, the object moves with a new constant speed. This transferred energy is known as kinetic energy. Kinetic energy depends on the mass and speed achieved and is a scalar quantity. The SI unit of kinetic energy is Joule whereas the CGS unit of kinetic energy is erg. There are different forms of kinetic energy including vibrational(the energy due to vibrational motion), rotational(the energy due to rotational motion), and translational(the energy due to motion from one location to another).

## Kinetic Energy Equation and Derivation

The mathematical expression for kinetic energy is,

K.E. = 1/2 m v2

Where,

KE —> Kinetic Energy

M —> Mass of the body

V —> Velocity of the body

The kinetic energy expression states that the kinetic energy of an object is directly proportional to the square of its speed. This means that for a twofold increase in speed, kinetic energy will increase by a factor of four. For a threefold increase in speed, the kinetic energy will increase by a factor of nine and similarly for a fourfold increase in speed, the kinetic energy will increase by a factor of sixteen. The kinetic energy is dependent upon the square of the speed.

Now, let’s derive the kinetic energy expression. For this, consider an object of mass m moving with uniform velocity u. Let us displace the object by s due to the constant force F acting on it.

Work done on the object of mass m is given by,

W= F x S —> 1

Now, the velocity changes to v due to the force and the acceleration produced is ‘a’.

In motion, we have a relationship between v, u, a, and s. This relationship is,

V²-U² = 2as

s = (v2 – u2)/2a  ——-> 2

Now, F= ma —> 3

Substituting equation 3 and equation 2 in equation 1, we have,

W = F × S

= ma x v²-u²/2a

W = 1/2 m(v²-u²)

When the object is at rest, i.e., if u=0, then,

W = 1/2 m v2

Hence,

K.E. = 1/2 m v2

## Kinetic Energy Examples

Some of the real life examples of kinetic energy are listed below,

• Running, walking, jogging, bicycling, swimming, and dancing
• Throwing a ball
• Launching a rocket
• Dropping an object or falling down
• A spinning windmill
• Driving a car
• Movement of clouds in the sky
• Playing with a yo-yo
• The blowing of wind
• The flow of electricity through a wire
• The movement of sound from speaker to your ears
• A meteor falling to earth

## Calculation of Kinetic Energy

Question 1. Calculate the kinetic energy of a 70 kg object that is moving at a speed of 1.3 m/s.

Solution. We have the equation for kinetic energy,

K.E. = 1/2 m v2

Given, m= 70 kg and v= 1.3 m/s. Now, substituting these values into the equation, we have,

KE= ½ x 70 x 1.3²

Hence, KE= 59.15 J

Question 2. Calculate the mass of an object moving at a speed of 30 m/s and having a kinetic energy of 1000 J.

Solution. Here we have to find out the mass of the object. So first consider the equation of kinetic energy.

K.E. = 1/2 m v2 ——-> 1

From this equation, we can rearrange the terms and formulate the expression for mass. Hence, we have,

m = 2KE/v² ——–> 2

From the question we have, KE= 1000 J and v= 30 m/s. Now substituting these values into equation 2, we have,

m= 2 x 1000/30²

Hence, m= 2.22 kg.

Answer. The kinetic energy of an object is defined as the energy it possesses by virtue of its motion.

K.E. = 1/2 m v2

Where,

KE —> Kinetic Energy

M —> Mass of the body

V —> Velocity of the body

Answer. Driving a car and dropping an object

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