What is negative mechanical energy?

As Kyle implies in the comments, mechanical energy is generally defined only up to a constant. Therefore, if you choose your constant as a large, negative number, you could have a total energy that is negative even with a very fast moving particle. read more

Mechanical Energy is the sum of potential energy and kinetic energy . Kinetic Energy can never have a negative value ( considering mass is non negative ) because of the term velocity( v²) . Coming to potential energy , it depends on reference line ( i.e. the line where you have considered zero P.E. ) . read more

Potential energy is also positive because $g=9.8$ and height is a distance, which is also non-negative. And yet, the problems says that the answer is true, as in the total mechanical energy is allowed to be negative. read more