Question

Derive the equation EK =1/2

MV^2 mathematically​

Answer 1

Answer:

Let a particle move from one point to another point separated by distance 'd' in time 't'.

Also, let's assume that particle starts with initial velocity '0' and final velocity 'v', and it has constant acceleration 'a'.

From first equation of motion, a= (v-0)/t = v/t

And distance travelled, d = (0)t + 1/2 at² = 1/2 at² = 1/2 v/t * t² = 1/2 vt

Work = Fd = (ma)d = mv/t * 1/2 vt = 1/2 mv²

By Work - Energy Theorem,

Change in Kinetic energy, KE - 0 = Work done

Therefore, KE = 1/2 mv².