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

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Answer 1 · 2018-01-20T23:52:44

See below.

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#