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A particle with a mass m = 2.00 kg is moving along the x axis under...

A particle with a mass m = 2.00 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 = 6.40 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 = 5.20 m: =_____ J.

(c) kinetic energy of the particle at the position x = 5.20 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 = 5.20 m: (Indicate the direction with the sign of your answer.)=_____m/s2

(f) maximum position the particle may obtain along the x axis: =_____m.

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