Pc John Dougal, 41, accelerated to 94mph (151km/h) in a 30mph zone before he hit Hayley Adamson in Newcastle's Denton Road on 19 May last year.
He was jailed for three years on Friday after earlier being convicted at Newcastle Crown Court.
Dougal was chasing a suspect car at the time, but did not have his siren or blue lights switched on.
During his trial it emerged Dougal was reacting to the automatic number plate recognition system of his Volvo patrol car, which alerted him to a passing Renault Megane.
But the device was incorrect and the Megane was being lawfully driven.