How to prove equation of kinetic energy (KE = 1/2mv^2)?
The work done is accelerating an object is given by:
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: