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A particle with a mass m = 4.00 kg is moving along the x axis under the influence of the potential energy function U(x) = (2.00 J/m²)x² -32.0 J. If the particle is released from rest at the position x = 7.00 m, determine the following. (The sign is important. Be sure not to round intermediate calculations.) (a) total mechanical energy of the particle at any position J (b) potential energy of the particle at the position x = 5.40 m (c) kinetic energy of the particle at the position x = 5.40 m J (d) maximum speed of the particle as it travels along the x axis m/s (e) acceleration of the particle at the position x = 5.40 m (Indicate the direction with the sign of your answer.) m/s2 (f) maximum position the particle may obtain along the x axis m