Piotr,

Fundamental to the notion of physics is the idea that the dimensions on one side of the equation must match those on the other.

On the left we have dimensions of energy.

You have m on the right with dimensions of mass, and t with dimensions of time.

What does the variable 's' represent?

And what is 'g'?

Do note that E=mc^2 is dimensionally balanced - any added terms must have dimensions of energy. Any scaling terms must be dimensionless.

Your proposed equation may not satisfy those needs - hence my above questions.

I proposed thath equation E=mc^2 is not satisfy but i did not have something equation which could replace them.

Piotr,

What is not satisfactory about it?

Please note that it is a specialized case of the more general frame-invariant description of the energy of a moving body:

https://bohr.wlu.ca/pc242/Phys242Lec5.pdf

E^2 = (pc)^2 +(mc^2)^2

As for the notion of 'dimensions', let me clarify.

I buy 2kg of apples, at 3 Euro per kg.

The cost, C (Euro), is found from the mass, m(kg), multiplied by the mass-specific cost, k (Euro per kg).

C = k.m

Here the dimensions balance: Euro on the left, kg multiplied by Euro per kg on the right. The 'kg's cancel, and I'm left with Euros on both sides.

This is an equation. The dimensions are 'equal'.

Any change, like C = k.m + t (if t is time in seconds, or any unit apart from Joules) cannot be correct.

Ignotum per ignotum E - general name of energy, c - type of energy. Then we could explain energy per some type of energy.

Piotr,

I confess, I do not understand what you wrote. Energy is the capacity to do work.

It has no other meaning in physics.

Can you rephrase your idea?

In either case, the quality of mass multiplied by a speed squared is identical to the quality of energy. The time-integral of power.