Question

How to prove equation of kinetic energy (KE = 1/2mv^2)?

Answer 1

See below.

Explanation:

The work done is accelerating an object is given by:

`W=FDeltax`

Where `F` is the force and `Deltax` the displacement.

If the object started from rest and all of the work was converted to kinetic energy then this will be equal to the kinetic energy of the object:

`K = FDeltax`

Using Newton's 2nd law:

`K = maDeltax=m(aDeltax)`

Now using the equation of motion:

`2aDeltax=v^2-v_0^2->aDeltax=v^2/2-v_0^2/2`

Substitute this into the equation for kinetic energy to get:

`K = m(v^2/2-v_0^2/2)`

If the object started from rest then the initial velocity will be:

`v_0=0` so `K` simplifies to:

`K = (mv^2)/2`