Question

1.a) Derive an expression for Kinetic Energy.​

Answer 1

a body of mass m is moving with velocity v. It is brought to rest by applying a retarding force F. Suppose it traverses a distance s before coming to rest. Kinetic energy of body, KE = Work done by retarding force to stop it.

Answer 2

$\huge \purple A \purple N \purple s \purple W \purple e \purple \R :-$

The kinetic energy of a body is the energy that it possessed due to its motion. Kinetic energy can be defined as the work needed to accelerate an object of a given mass from rest to its stated velocity. The derivation of kinetic energy is one of the most common questions asked in the examination. Students must understand the kinetic energy derivation method

properly to excel in their examination.

Kinetic energy depends upon the velocity and the mass of the body. If the velocity of the body is zero, then the kinetic energy will also be zero. The derivation of kinetic energy is given below so that students can understand the concept more effectively. the kinetic energy formula derivation can be done using algebra and calculus. Both the methods are explained below.

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

DERIVATION OF KINETIC ENERGY USING ALGEBRA

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

∆K = W = F∆s = ma∆s

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

v^2 = v0^2 + 2a∆s

a∆s = v^2 - v0^2 / 2

Combining the 2 expressions we get,

∆K = ( v^2 - v0^2 / 2 )

∆K = 1/2mv^2 - 1/2mv0^2

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:

K.E = 1/2mv^2