**What is Kinetic Energy?**

**Definition: **When a body is capable of doing work by virtue of its motion, the energy is called kinetic energy, or the energy associated with a mass due to its motion is called** kinetic energy**.

**Examples Of Kinetic Energy:**

We can see kinatic energy examples in our our surrounding, also in our home

- A walking and running boy
- Moving Car
- Cycling
- Wind Mills
- Skateboarding
- Dropping a bowl on the floor

**Kinetic Energy Formula**

**K.E = 1/2mv²**

where m stand for mass, and v is velocity. The velocity in this formula is squared, which means that it is exponential.

**How to Calculate Kinetic Energy / Formula Derivation**

To obtain an expression for K.E we have to determine the work done by the body in motion. This work is equal to the Kinetic energy of the body. Consider a body of mass ‘m’ placed on a horizontal surface initially at rest. When a force `F' is applied, it covers a distance`

S’ and its final velocity becomes “v”. Work done is covering the displacement S.

W = F.S ——————————- (i)

But by the second law of motion, when a force acts on a body, it produces acceleration in the direction of the force

F = ma ———————— (ii)

And by using the equation of motion

i.e v1² – v1² = 2aS

When vi = 0, vf = v and s =?

∴ v² – 0 = 2as or s = v² ÷ 2a ——————– (iii)

Putting the value of ‘F’ and’s’ in equation (i)

Work = K.E = F.S = ma x v² ÷ 2a

∴ K.E = mv² ÷ 2 = 1 ÷ 2mv²

K.E = 1 ÷ 2mv² or 1/2mv²

The equation shows that the Kinetic energy of a body is directly proportional to its mass and also to the square of its velocity. If two locomotives move with the same velocity then the K.E of the locomotive which has a large mass is greater than the other. If, however, two cars of the same mass move with different velocities, then the one having greater velocity will possess greater kinetic energy.

**Kinetic Energy Problems or Kinetic Energy Questions**

**Example 1:**

**A boy of mass 50Kg on a motorbike is moving with 20 m/s. What is his K.E?**

**K.E = 1/2mv ²**

K.E = ½(50)(20) ²

K.E = (0.5)(50)(400)

K.E = 10000J

**Example 2:**

**A 30 gram bullet travels at 300 m/s. How much kinetic energy does it have?**

**K.E=1/2mv²**

m= 30 gram = 30/1000 = 0.03kg

v=300ms

K.E = 1/2(0.03)(300)²

K.E=(0.5)(0.03)(90000)

K.E= 1350J

**Example 3:**

**A 70 Kg man runs at a pace of 4 m/s and a 50 gram meteor travels at 2km/s. which has the most kinetic energy?**

**K.E=1/2mv²**

**Man’s Kinetic Energy:**

K.E=1/2(70)(4)²

K.E=(0.5)(70)(16)

K.E=560J

**Meteor Kinetic Energy:**

m=50 g = 50/1000 = 0.05kg

v= 2km/s = 2000m/s

K.E= 1/2(0.05)(2000)²

K.E= (0.5)(0.05)(4000000)

K.E=100000J

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