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

##### 1 Answer

Jan 20, 2018

See below.

#### Explanation:

The work done is accelerating an object is given by:

Where

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:

Using Newton's 2nd law:

Now using the equation of motion:

Substitute this into the equation for kinetic energy to get:

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