Question

derivation of kinetic energy?

Answer 1

The relation connecting the initial velocity (u) and final velocity (v) of an object moving with a uniform acceleration a, and the displacement, S is v2 - u2 = 2aS This gives S = v 2 - u 2 /2a We know F = ma. Thus using above equations, we can write the workdone by the force, F as W = ma v 2 - u 2 /2a or W = 1 /2 m( v 2 - u 2 ) If object is starting from its stationary position, that is, u = 0, then W = 1 2 m v 2 It is clear that the work done is equal to the change in the kinetic energy of an object. If u = 0, the work done will be W = 1 2 m v 2 . Thus, the kinetic energy possessed by an object of mass, m and moving with a uniform velocity, v is Ek = ½ mv2

Answer 2

Consider an object of mass, m moving with a uniform velocity, u. Let it nowbe displaced through a distance s when a constant force, F acts on it in the direction of its displacement

the work done, W is F s.W = F.S = ma sThe work done on the object will cause a change in its velocity.Let its velocity change from u to v.Let a be the acceleration produced.

v²-u²=2as
s=v²-u²/2a

F =ma

W = ma× v²-u²/2a
W = mv²-u²/2a

u = 0 (as the object starts at rest)

Ek = 1/2 mv²