What is Kinetic Energy?

The energy possessed by an object due to its motion in any direction (horizontal or vertical) is known as kinetic energy. In simple words, we can say that it is the energy of motion. So, every moving object around us possesses kinetic energy. Further, the kinetic energy of an object is due to the net work done on it as no object can move and cover the distance without applying a force on it.

Formula of Kinetic Energy

The formula of kinetic energy shows the relation of energy with mass (m) and velocity (v).

The kinetic energy of an object of mass 'm' moving with velocity 'v' is given by

Kinetic energy = ½ mv²

m = mass of the object in motion

v = speed of the object

So, the kinetic energy of an object can be calculated as half its mass times the square of its velocity (v). Kinetic Energy is a scalar quantity so it does not depend on the direction and thus its value will always be positive.

As we know energy is the capacity to do work and kinetic energy is also a type of energy, so the above formula of kinetic energy is the expression of the fact that a moving object has kinetic energy that can do work on anything it hits. The above formula tells the amount of work a moving object can do as a result of its motion.

The above formula also shows that K.E is directly proportional to the mass and square of the velocity of the object. So, if we double the mass, the energy will get doubled and if we double the velocity, it will be four times the previous value. For example, a moving truck at twice the speed will have four times the kinetic energy. For example, a truck moving at 50 kmph will have four times the kinetic energy of the same truck moving at 25 kmph. So, a large truck will have more kinetic energy than a small truck and will cause more damage when it hits something.

Kinetic energy can be transferred from one object to the other or between objects. Further, it can be transformed into other types of energy. For example, if a moving car collides with a stationary object then some of the kinetic energy of the car gets transferred to the object or transformed into another type of energy.

Kinetic Energy Units

The SI unit of kinetic energy is the joule (J), which is equal to 1 kg.m².s-². It is also a type of energy and the unit of energy in the metre-kilogram-second system is the joule. For example, a 2 kg object moving at a speed of 1 m/s will have a kinetic energy of 1 joule.

As per the centimetre-gram-second system, the unit of energy is the erg, 10^-7 joule, which is equal to the kinetic energy of a mosquito flying in the air.

Facts about Kinetic Energy

• The value of kinetic energy is always positive. Although the value of velocity can be positive or negative, the value of the square of velocity is always positive.
• Kinetic energy is a scalar quantity, not a vector. So, a car moving to the north with a speed of 50 kmph will have the same kinetic energy as a car moving in the south direction or any other direction with the same speed.
• The kinetic energy of a moving object remains unchanged unless the speed or mass of the object is changed.

Deriving Kinetic Energy Equation or Formula

The kinetic energy equation or formula can be derived from the work done (w) by a force (f) on an object. For example, a body of mass 'm' is pushed by applying force 'f' and it covers a distance 'd' on a surface, this the work done on the object makes it move and due to movement it possesses kinetic energy, so work done in this case, is equal to kinetic energy or can be used to derive kinetic energy equation.

W = F. d (force . displacement )

Now f = m . a ( mass . acceleration)

So, after putting the value of f, we have

W = m . a . d ( mass x acceleration x displacement)

As per the third equation of motion, the acceleration is given by;

a = v² - u²/ 2d

v = final velocity of object

u= initial velocity of object

d = displacement

now, after putting the value of a, we have;

W = m. d. v² -u² / 2d

W = m . v² -u² /2

Let the initial velocity 'u' is zero, as the object was at rest before force is applied to it. So, on simplifying the above equation, we get;

W = m . v² /2 or ½ mv²

As work done is equal to kinetic energy, so, we get;

KE = ½ mv²

From the above equation, it is clear that the total work done on a system or an object is equal to the change in kinetic energy if it starts moving.

So, W_net = ∆ K (net work done = change in kinetic energy)

Solved Examples:

1. Find the kinetic energy of a 100 kg object moving at a speed of 10 m/s.

Solution: K.E can be calculated using the following equation:

KE = ½ mv²

KE = ½ (100 kg) (10 m/s) ²

= 50 x 100 = 5000 J

Similarly, if we know the kinetic energy and velocity of speed, we can calculate the mass of the object as shown in the below-solved example;

2. Find the mass of a car travelling at a speed of 50 m/s and has a kinetic energy of 2000 J.

Solution:

KE = ½ mv²

After rearranging the above equation, we get

m = 2KE/v²

After substituting the given values, we get

m = 2 x 2000 / 50² = 1.6 Kg

Similarly, we can calculate the speed of an object if we know its mass and kinetic energy as shown in the below-solved example;

3. A 500 kg boat has a kinetic energy of 2000 J. Calculate the speed at which it is moving?

Solution:

KE = ½ mv²

After rearranging, we get

V² = 2 KE /m

V² = 2 x 2000 / 500 = 2.8 m/s

Examples / Uses of kinetic energy

1. Hydropower plant: Electricity is generated in hydropower plants using moving water. The moving water has kinetic energy due to its motion and when it hits the turbines and turbines start moving. So, we can say that the kinetic energy of water is transformed into mechanical energy as the turbines start moving to produce electricity.
2. Windmills: The windmills work by using the kinetic energy of the winds. The wind which is in motion hits the blades and the blades start moving which leads to the generation of electricity. Here, the kinetic energy of wind gets converted into mechanical energy.
3. Bullet from a gun: The bullet fired from a gun also has tremendous kinetic energy. Although its mass is less, it can pierce any object due to its high velocity as kinetic energy also depends on velocity.
4. Aeroplane or fighter jets: A flying plane has both large mass and high velocity, so its kinetic energy is very high as both factors mass and velocity are directly proportional to the kinetic energy.
5. Moving vehicles: All moving vehicles like cars, bikes, and cycles possess kinetic energy due to their speeds. The only difference is that a light vehicle due to its less mass has less kinetic energy than a large vehicle like a car.
6. Walking and running: When we run or walk we are in motion so we possess some amount of kinetic energy. This is also the reason that we feel warm while running. In this case, chemical energy is getting converted into kinetic energy.
7. Bicycle: While riding a bicycle, we have to pedal it to make it move. Here, the potential energy of our body changes into mechanical energy, which further gets converted into kinetic energy possessed by the moving bicycle.
8. Rollercoasters: The potential energy of the wagon of a roller coaster is converted into kinetic energy. At the top, the kinetic energy of the wagon is zero and the potential energy is maximum when it starts a free fall, the potential energy is gradually converted into kinetic energy which makes it move at a high speed.
9. Cricket ball: The kinetic energy of a cricket ball is zero when it is in the hand of a bowler as it is at rest and not moving. But, when the bowler throws the ball toward the batsmen, it possesses kinetic energy due to its mass and speed. The batsman and wicket-keeper have to wear safety gear so that they do not get hurt as the ball's kinetic energy usually is very high.
10. Skateboarding: A boy who rides a skateboard possesses kinetic energy. At rest, the kinetic energy is zero, however, when he starts riding, the kinetic energy starts increasing.
11. Waterfall: A waterfall that falls from a mountain on the ground also possesses kinetic energy. The potential energy of the waterfall is converted into kinetic energy in this case.