Can mechanical energy of a moving particle be negative

Yes mechanical energy can be negative.

You cannot have negative energy;

You can have a certain quantity of energy or none at all but it is impossible in reality to have negative energy;

In terms of equations however, you can have a positive or negative sign, this tells us whether energy is gained or lost

increasing transnational kinetic energy. because the transnational kinetic energy formula consists of only two variables, mass and velocity, increasing one of those properties is the only way to increase an object's transnational kinetic energy. increases to mass and velocity, however, do not have the same impact.