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    $\begingroup$ What is the problem with kinetic energy being able to go positive because the potential energy can go negative? It is perfectly fine for mechanical energy to be zero, or negative, and yet have things move. Nothing is wrong here. $\endgroup$
    – naturallyInconsistent
    Commented Feb 18 at 11:31
  • $\begingroup$ ok but then it will be hard to find questions like maximal height, if we apply conservation of mechanical energy at maximal height all the kinetic energy is turned into potential energy but then we have both of them initially null so how to proceed $\endgroup$
    – dddr rddd
    Commented Feb 18 at 11:36
  • $\begingroup$ No, it is not going to be difficult. There is a minimum of the potential energy, in this case being some size of negative number, and that size of energy will then be the kinetic energy; Similarly, the kinetic energy has a minimum of zero, and when that happens, you can find the maximum of the potential energy, which will determine the maximal height. You are just not familiar with this, it is not difficult. $\endgroup$
    – naturallyInconsistent
    Commented Feb 18 at 11:43
  • $\begingroup$ thanks for clarifying $\endgroup$
    – dddr rddd
    Commented Feb 18 at 13:40