 # Kinetic Energy Formula

Kinetic energy is an important topic in the field of Physics. Basically, it is the energy an object possesses because of its motion. This energy is dependent on the velocity of the object squared. So, when the velocity doubles, consequently the kinetic energy quadruples. Moreover, this energy should be either a zero or a negative value. Learn the Kinetic energy formula here.

## What is Kinetic Energy?

Kinetic energy refers to a form of energy which an object or particle has due to the motion. On the application of the net force on an object, the object speeds up and consequently generates this energy. This energy is a property of an object or particle which moves. Furthermore, this energy depends not only on the motion but also on the mass. This energy refers to the work required to accelerate a body of a particular mass from a state of rest to its stated velocity. Moreover, the same amount of work is required for decelerating from the current speed to a position of rest. Most noteworthy, the standard unit of this energy happens to be the joule. Also, foot-pound is the imperial unit of this energy.

## Kinetic Energy Formula

For the Kinetic formula, Ek, is certainly the energy of a mass, m, motion, of course, is v2.

Ek = 1/2 mv2

Ek = Kinetic energy

m = mass of the body

v = velocity of the body

### Kinetic Energy Formula Derivation

Let us consider the example of an object of m which is at a state of rest on a table.

A force F acts on the object which moves it through a distance S.

The work done=F x S

W=Fnet x S——-(1)

Consider the work done on the object which results in a change in velocity from u to V. Furthermore, one must let “a” be the acceleration.

Considering the third equation of motion:

V²-u²=2as

s=V²-u²/2a———-(2)

Applying Newton’s Second law:

F=ma——(3)

From equation (1), (2) and (3)

W=ma*(V²-u²/2a)\=(1/2)m(V²-u²)

As the object in a state of rest, u=0

W=(1/2)mV²

Furthermore, the kinetic energy of a body moving with a certain velocity is equal to work done on the object. This work is for the purpose of acquiring that velocity from the estate of rest.

Therefore, Kinetic energy =1/2 mV²

## Solved Examples on Kinetic Energy Formula

Q1 The mass of a bicycle is 10 kg, and it moves at a constant velocity of 10 km/h. Find out the kinetic energy of this bicycle?

A1 Here the mass is “m’ and the velocity is “v”. Also, m = 10 kg and v = 10 km/h. Now, one must apply the kinetic energy equation:

Ek = 1/2 mv2

Ek = 1/2 (10 kg) (10km/h)

Ek = 50 Joules

Hence, the kinetic energy, in this case, is 50 Joules.

Q2 The kinetic energy of the car is 300,000 Joules and its velocity is 30 m/s. Find out the mass of the vehicle?

A2 The kinetic energy of the car in motion is certainly Ek = 300,000 J = 30,000 kg m2/s2. Moreover, the velocity of the car which is v = 30 m/s

Ek = 1/2 mv2

Ek/0.5v2 = m

m = (300,000 kg m2/s2)/[0.5(30m/s)2]

m = (300,000 kg m2/s2/[(0.5)(900)m2/s2]

m = (300,000 kg m2/s2/450 m2/s2

m = 666.666 kg

Hence, the mass of the vehicle = 666.666 kg

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Typo Error>
Speed of Light, C = 299,792,458 m/s in vacuum
So U s/b C = 3 x 10^8 m/s
Not that C = 3 x 108 m/s
to imply C = 324 m/s
A bullet is faster than 324m/s Guest

I have realy intrested to to this topic Guest
umer

m=f/a correct this Guest
B. Akshaya

M=f/g Guest

Interesting studies Guest
Yashdeep tiwari

It is already correct f= ma by second newton formula… Guest
Xyz

Hi