Question

derive the fourmale ke = 1/2mv^2 where terms have their usal meaning

Answer 1

Energy posses by a body by virtue of its motion is referred to as ‘Kinetic Energy.

Now, it is represented by K. E., and bears a formula which can be represented as :

K. E. = 1/2 m v²

Consider a body of mass "m" with initial velocity ("u") = 0, covering a displacement of "s", acceleration "a", and acquiring final velocity "v".

Now, we know, v² = u² + 2 as

Putting the value of u, in its place, we get :

v² = 0² + 2as

Or, v² = 2as

Or, a = v²/2s

Also, F = ma

Again, W (work done) = Fs

Or, W = m.a.s [putting F = ma]

Or, W = m.(v²/2s).s

Or, W = 1/2 mv², which is the required mathematical expression for kinetic energy.

Since the work done is with motion, the work done is equal to "Kinetic Energy" attained by that body.