Derivation of Kinetic Energy: Overview, Questions, Preparation

Force is required to make an object move or accelerate, and for every work, there should be work associated with it. When work is done, an external force releases the object’s energy to accelerate it, and the object moves at a constant speed. The energy that is transferred in the object is known as Kinetic energy. In other words, kinetic energy can be described as the object’s energy while in motion.

The formula for kinetic energy shows the relationship between the mass of the body and the velocity of the body. It can be expressed as under:

K.E. = ½ mv²

Here,

• KE is the kinetic energy
• m denotes the mass of the body
• v denotes the velocity of the body

There are five types of Kinetic energy, which are listed below:

1. Radiant energy
2. Thermal energy
3. Sound energy
4. Electrical energy
5. Mechanical energy

Kinetic energy can be derived in a couple of ways, but algebra is considered the best way to fully understand the formula.

By using the work-energy theorem and the second law of Newton, the following equation will be formed:

• ΔK = W = FΔs = maΔs

After integrating it in kinematic equations, we will get:

On combining both the equations, we get

As we discussed above, the kinetic energy is held by virtue of its motion, and it will be zero when it is at rest position. So, we can say that:

• KE = ½ mv²

The derivation of kinetic energy can be calculated using the calculus method by using the work-energy theorem and the second law of Newton. In the calculus method, we just assume the acceleration of the object. After rearranging the work-energy theorem to get the function of the differential terms, we will get the final formula of kinetic energy as we did in the algebra method.

Example 1) Write the types of Kinetic Energy.

Answer – There are five types of Kinetic energy, which are listed below:

1. Radiant energy
2. Thermal energy
3. Sound energy
4. Electrical energy
5. Mechanical energy

Example 2) Write two examples of thermal and sound energy.

Answer – Hot springs and heated swimming pools are examples of thermal energy. On the other hand, the tuning fork and the beating drums are examples of sound energy.

Example 3) Write the meaning of Electrical energy.

Answer – Electrical energy can be defined as the combination of positive and negative charge-free electrons.