Sped and speeded are both dictionary-approved inflections of the verb to speed, and neither is more correct than the other. The old rule says speeded works only in the phrasal verb speeded up, but this recommendation is dated (though some traditionalists continue to spread it). In practice, writers generally use whichever they think sounds best. Speeded is widely used without up, and sped is likewise used both alone and with up. Sped is about three times as common as speeded not because it’s more grammatically correct but because it’s briefer.
Examples
Edited publications from throughout the English-speaking world use sped and speeded interchangeably. Speeded is used both on its own and without up—for example:
… Al Jazeera’s relentless coverage speeded his messy slide to extinction. [The Economist]
… Mel Blanc’s voice was speeded up by 20% to get the little bird’s high-pitched tone, said his son. [Los Angeles Times]
Mr Spriggs … is also acutely aware of contrasts between the interventionism which speeded Team Valley’s development … [Financial Times]
All that has happened is that, at a time of economic crisis, this process has been speeded up. [The Australian]
And sped is also used both on its own and as part of a phrasal verb—for example:
The driver then climbed back into his car and sped away. [Edmonton Journal]
Beijing-based Gome has sped up its expansion by opening more stores in second- and third-tier Chinese cities … [Wall Street Journal]
A 14-year-old girl who sped past a patrol car led police on a short pursuit … [The Canberra Times]
She has sped up urban works in many cities and towns in Uttar Pradesh. [BBC]

