Question

how to derive formula of kinetic energy​

Answer 1

Answer:

Derivation of Kinetic Energy using Algebra

The kinetic energy derivation using only algebra is one of the best ways to understand the formula in-depth.

Starting with the work-energy theorem and then adding Newton’s second law of motion we can say that,

Derivation Of Kinetic Energy

Now, taking the kinematics equation and rearranging it, we get

Derivation Of Kinetic Energy

Combining the 2 expressions we get,

Derivation Of Kinetic Energy

Derivation Of Kinetic Energy

Now we already know that kinetic energy is the energy that it possessed due to its motion. So the kinetic energy at rest should be zero. Therefore we can say that kinetic energy is:

Derivation Of Kinetic Energy

Derivation of Kinetic Energy using Calculus

The derivation of kinetic energy using calculus is given below. To derive an expression for kinetic energy using calculus, we will not need to assume anything about the acceleration.