Question

Derive K. E. =1/2mv^2

Answer 1

latest considered mass M at rest that is initial velocity of object of mass M is zero when a constant force is applied on the object it displaces the object,through a distance S in the direction of force

The work done W is given by

W=f×s------------(1)

this work done on the object will cause a change in its velocity from zero to V

Let a to be acceleration produced in the body in the direction of applied force.
According to Newton second law of motion F=m×a---------(2)

FROM THIRD EQUATION OF MOTION

V^2-U^2=2as------------(3)

V^2=2as

S=v^2/2a

From (1),(2),&(3)

W=ma ×v^2/2a

(by cancelling from 'a' to 'a')

Then it is proved


K. E. =1/2mv^2








NoTE:::Diagram is also compulsory and u have to draw it after first paragraph