Naomi Anna Colcomb, 28, died after being being by a grey Fiat Bravo while crossing St Mary's Gate at around 1.50am on Saturday, October 13, following a night out with friends.
Her mother Sabine Heiliger said she had been watching old episodes of Star Trek at a friend's house before heading to a gig.
She was walking home at the time of the collision.
Making an appeal to the public at a press conferenceÂ last week, Sabine said:Â 'I don't know what words I can use. It's left a huge hole inside me and I just don't understand what's happened.
'I would like to know anything. I would love to know what she was doing and who saw her just before she died.'
Ms Heiliger said Naomi, who worked as a service manager of a kitchen design company, was a keen volunteer, often helped the homeless and was a campaigner against food waste.
She was engaged and had lived in Sheffield for almost four years.
Ms Heiliger said: 'She loved Sheffield. She loved the people who were all very friendly and lots of people will have seen her about because she was always walking everywhere.
'She always had a smile and was very, very caring. She would not walk past anyone who was homeless.'
Naomi, who was the youngest of four siblings, died at the scene of the collision, despite efforts from passers-by who tried to save her following the impact.
Two men '“ aged 51 and 24 '“ have both been arrested on suspicion of causing death by dangerous driving but have both been released under investigation.
Sgt Roden said the front of the car was damaged on the driver's side and the headlight was also not working as a result of the collison.
Anyone with any information should call police on 101, quoting incident number 98 of October 13 or call Crimestoppers, anonymously, on 0800 555111.