prove work energy theorem for a variable force
Dear Student!!
Suppose,
m = Mass of a body
u = Initial velocity of the body
v = Final velocity of the body
a = Acceleration
ki = Initial kinetic energy of the body
kf = Final kinetic energy of the body
The rate of change of kinetic energy is,
dk = Fdx
On integrating from the initial position (xA) to the final position (xB), we have
[From equation (i)]
∴Work done on the body = Increase in K.E. of the body