Question

what will be the new kinetic energy of a body if its velocity is doubled

Answer 1

its kinetic energy will be four times of initial

Answer 2

Normally we write ,

Kinetic Energy = 1/2mv^2

Now you said to double the velocity
Hence the new velocity will be 2v

So now the
Kinetic energy = 1/2m(2v)^2
= 1/2m4v^2
= 2mv^2

It's been clear from the observation that KE gets four times if velocity is doubled.