Question

What is kinetic energy? Deduce an expression for the kinetic energy of a body of mass m moving with a velocity v

Answer 1

Suppose a body of mass  m  is moving with a uniform velocity  u . Let an external force be applied on it so that it gets displaced by distance  s  and its velocity becomes  v . In this scenario, the kinetic energy of the moving body is equal to the work that was required to change its velocity from u  to  v .

Thus, we have the velocity−position relation as:

v 2  =  u 2  + 2 as

OR



Where,  a  is the acceleration of the body during the change in its velocity

Now, the work done on the body by the external force is given by:

W  =  F  ×  s

F  =  ma …(ii)

From equations (i) and (ii), we obtain:



If the body was initially at rest (i.e.,  u  = 0), then:



Since kinetic energy is equal to the work done on the body to change its velocity from 0 to  v , we obtain:



Answer 2

Hope this helps you buddy