What is the acceleration profile of the greyhound?
I'm going to try to break this up a bit to address your sub-questions. Most of it is summarized from Williams et al 2008--and almost all of the work I'm referencing comes from the Royal Veterinary College Structure and Motion Lab.  

Acceleration Profiles:

So, I can't find an acceleration curve over time for these, but we do know about the potential acceleration range for greyhounds and cheetahs. Greyhounds can reach a max speed of about 17 m/s (Usherwood and Wilson 2005), cheetahs can reach up to 29 m/s (Hudson et al. 2010). Cheetah stride-averaged accelerations have been measured up to 120 W/kg --they can speed up by 3 m/s over a single stride, and slow down by up to 4 m/s (Wilson et al. 2013). Racing greyhounds have achieved 60 W/kg (Williams et al. 2009).  Maximum acceleration decreases with increasing speed

How Land Animals Can Be Fast


Augmentation or hypertrophy of proximal musculature. More than a fifth of a greyhound's limb muscle mass is associated with the proximal portion of the hindlimb (Williams et al. 2008). Muscle power (work/time, important for acceleration) is roughly proportional to muscle volume, so bigger muscles are better in this case.  In cheeetahs, a similarly large muscle mass is devoted to hip extensors (though different specific muscles; Hudson et al 2010). Big muscles = high power and high force production.  In addition, sprinting mammals tend to have longer muscle moment arms than non-sprinters--so they can produce greater torques for a given force. 
Longer muscle fascicles. This may also be an adaptation for power output. Greyhounds have longer fascicle lengths in their hamstrings than your average domestic dog (Williams et al 2008), and human sprint athletes also have longer fascicle lengths than endurance runners (Abe et al. 2000). 
Long limbs and flexible spines: Longer limbs w/ spinal flexion = greater stride length--and cheetahs have particular elongated hind limbs. A long hind limb also lets cheetahs maintain foot contact with the ground for longer, so lower peak forces are required. 


These aren't nearly all of the things involved, but I suppose this is a start. 

References: 


Abe, T., K. Kumagai and W.F. Brechue. 2000. Fascicle length of leg muscles is greater in sprinters than distance runners. Med. Sci. Sports. Exerc. 32: 1125-1129. 
Hudson, P. E. et al. 2010. Functional anatomy of the cheetah (Acinonyx jubatus) hindlimb. J. Anat. 218: 363–374.
Usherwood, J. R. and A. M. Wilson. 2005. No force limit on greyhound sprint speed. Nature. 438, 753-754.
Williams, S.B. et al., 2008. Functional anatomy and muscle moment arms of the pelvic limb of an elite sprinting athlete: the racing greyhound (Canis familiaris). J. Anat. 213:  361–372.
Williams, S. B. et al. 2009. Pitch then power: limitations to acceleration in quadrupeds. Biol. Lett. 5: 610-613.
Wilson, A. M. et al. 2013. Locomotion dynamics of hunting in wild cheetahs. Nature. 498: 185-189.