An experimental form of cancer therapy involves the use of a beam of highly ionized carbon atoms with a charge of +6e (all six electrons have been removed). The mass of the ions is 11.172 GeV/c². If the accelerator is 7.50 m long and the ions are accelerated through a 125 MV potential difference, what are 

(a) The ion's kinetic energy, 

(b) The speed of the ions as measured in the lab frame, and 

(c) The length of the accelerator in the reference frame of the ions?