Derive the relation between momentum and kinetic energy.

Explanation

Consider an object of mass m moving with a velocity `vecv`. Then its linear momentum is `vecp=mvecv` and its kinetic energy, `KE=(1)/(2)mv^(2)`
`KE=(1)/(2)mv^(2)=(1)/(2)m(vecv.vecv)" "...(1)`
Multiplying both the numerator and denominator of equation (1) by mass, m
`KE=(1)/(2)(m^(2)(vecv.vecv))/(m)`
`=(1)/(2)((mvecv).(mvecv))/(m)[because vecp=mvecv]`
`=(1)/(2)(vecp.vecp)/(m)=(p^(2))/(2m)`