Question

What is work energy theorem? Derive the expression of Kinetic energy with relation to work energy theorem?

Answer 1

Dear student
WORK ENERGY THEORAM states that the work done by the particle is equal to the change in the particle's kinetic energy.
$W=∆K.E.$

EXPRESSION FOR KINETIC ENERGY
consider a body of mass m moving with the initial velocity u .let the force be F ,work done is W and distance covered by it is s. From NEWTON's SECOND LAW OF MOTION

F = ma ------ eq.1

and work done by the body is W = F.s ------- eq .2
third law of motion is $v^2-u^2=2as-----eq3$

from eq. 1,2and 3

W = ma $\times \frac{v^2-u^2}{2a}=\frac{m(v^2-u^2)}{2}$
$$\begin{gathered} W=\frac{1}{2}m{v}^2-\frac{1}{2}m{u}^2 \\ astheobjectstartedfromrestu=0 \\ W=\frac{1}{2}m{v}^2 \end{gathered}$$
which is the kinetic energy.
this shows that work stored by a moving object is called the kinetic energy of the object.

Regards