Douglas Fraser, 40, accelerated towards Brien Foster, 28, and smashed into him as he tried to jump out of the way.
A woman in a nearby flat at Edinburgh's Portobello Road heard the noise of a car skidding and looked out of her window to see Mr Foster lying injured in the carriageway.
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Hide AdAt an earlier hearing, fiscal depute Graeme Jessop said the injury had left Mr Foster with speech and memory problems. He added that Mr Foster had no recollection of the incident.
Fraser was traced through CCTV footage and his employer, City Cabs. Fraser, of Roull Road, Corstorphine, admitted driving dangerously and hitting Mr Foster to his severe injury and permanent impairment. He also admitted failing to stop after the accident which happened on December 2 last year.
Sheriff Kenneth Maciver said that custody was the only option. Fraser was also banned from driving for three years and ordered to sit the extended driving test.