Question

derive the expression for kinetic energy

Answer 1

Consider an object of mass 'm' moving with an intialy velocity'u'. A constant force 'F' act on an object. The velocity of the object changes to 'v'.


v2-u2=2as
s=v2-u2/2a
w=F×S
w=ma×s
w=ma×(v2-u2/2a)
w=1/2m(v2-u2)
u=0
w=1/2mv2
KE=1/2mv2

Answer 2

hey mate your answer
Suppose a Force ‘F’ acting on a body of mass ‘m’ in state of rest changes its velocity to ‘v’ and body covers ‘s’ distance in the direction of force.



Then, the work done by the force is given by

W = F . S

= ma . S …………(1) [ F = ma ]

Now, using equation of motion, we have

v2 = u2 + 2aS

or, v2 = 0 + 2aS

as = v2/2

So, by equation (1) , we get

W = m .v2/2

so , by definition of kinetic energy of the body,

K.E. = W = 1/2 mv2