Kinetic Energy - use a log scale or not? [closed]

Question

Lets say we have a series of balls and an eggs. All items have equal mass but are traveling at different velocities.

Thus they have differing kinetic energies.

Now, for each 'ball' object we have, we want to find an egg object with a similar kinetic energy. Lets say, within +-1 standard deviation interval

Would it be correct to take the kinetic energy as it is and use the linear interval of 1SD, or convert to the kinetic energy to a logarithmic scale

My guess is to use a log scale as Kinetic energy does not increase linearly with speed

Answer 1

Or you could just use the square of kinetic energy $\sqrt K$ instead of $K$ to have a linear relationship with speed. I am not sure why you would use a log-scale - the relationship is not logarithmic.