Kinetic energy :
The energy possessed by an object due to its motion is called kinetic energy.
Numerical expression for K.E.:
1) Let us assume that an object of mass (m) is at rest on a smooth horizontal plane as shown in figure.
2) Let be displaced through a distance ‘s’ from the point A to B by a force (F) acting upon it in the direction of the displacement.
3) In the horizontal direction the net force ‘Fnet ‘ is equal to the force applied ‘F’.
∴ W = Fnet.s = F.s …………. (1)
4) Let the work done on the object cause a change in its velocity from ‘u’ to ‘v’ anr the ‘acceleration produced be ‘a’.
5) We know that v - u = 2as ⇒ s = \(\frac{v^2\,-\,u^2}{2a}\)..............(2)
6) From Newton's second law of motion , F = ma ..............(3)
7) From (1) , (2) and (3)
W = \(\frac{ma(v^2\,-\,u^2)}{2a}\)
W = \(\frac{1}{2}m(v^2\,-\,u^2)\)
8) As we Have assumed that object is at rest, then the initial velocity u = 0.
∴ W = 1/2 mv2
9) We know that K.E. of a body moving with certain velocity is equal to work done on the object to acquire that velocity from rest.
10) Thus the K.E. of an object of mass ’m’ and moving with velocity V is equal to K.E = 1/2 mv2
