How to solve for this question?

Question

Derive an equation for the kinetic energy of particle expressed as a function of its momentum.

Answer 1

I agree with both the above answers, to an extent, and wouldn't want you to suggest this to the person who set the question unless you are very confident, but you really can't 'derive' anything unless you have defined given or assumed truths ( aka facts ) from which to derive it.

Answer 2

KE=(1/2)mv^2, P=mv

so, KE=(1/2)Pv

Answer 3

E=1/2mv^2=1/2mv.v=1/2pv...done.

Answer 4

Suppose the mass of a body be m and it's velocity be v.

Therefore momentum = mv

Kinetic energy =  mv^2/2

Multiply and divide the expression for kinetic energy by m

It becomes  K.E = (mv)^2/2m

                        = (momentum)^2/2m