110How do I derive expression for kinetic energy?Invest in your future! Advance your career in 12 months.Susmita DuttaAnswered July 11, 2017Expression for K.E - KINETIC ENERGY-K.E = 1/2 mv2. "Energy posses by a body by virtue of its motion is referred to as 'Kinetic Energy'". Kinetic energy depends upon the mass and velocity of body. If velocity is zero then K.E. of body will also be zero.Kinetic energy is a scalar quantity like other FORMS of energies.Consider a body of mass "m" STARTS moving from rest. After a time interval "t" its velocity becomes V.If INITIAL velocity of the body is Vi = 0 ,final velocity Vf = V and the displacement of body is "d". ThenUsing equation of motion2aS = Vf2 – Vi2Putting the above mentioned values2ad = V2 – 0a = V2/2dNow force is given byF = maPutting the value of accelerationF = m(V2/2d)As we know thatWork done = FdPutting the value of FWork done = (mv2/2d)(d)WORK done = mV2/2ORWork done = ½ mV2Since the work done is motion is called "Kinetic Energy"i.e.K.E. = Work doneORK.E. =1/2mV2