Mother-of-three Karina Menzies, 32, was knocked down and killed outside a fire station near her home in Cardiff.
Police are continuing to question a 31-year-old man in connection with her death, as well as investigating reports he deliberately ran people down in the Welsh capital with a white Iveco van.
Detective Superintendent Paul Hurley said: "We are aware the suspect assaulted people outside his vehicle."
He added that police were looking to identify and recover the weapon, believed to be a crook lock vehicle security device. It is thought the killer used it to assault witnesses.
Detectives yesterday confirmed the dead woman was among 14 people – seven children and seven adults – hit by the van during a period of 30 minutes.
Eleven were admitted to the University Hospital of Wales, where nine of those remain.
Two adults are fighting for their lives in intensive care, with both in a "critical but stable" condition.
The other victims are said to be suffering from mostly fractures and head injuries.
It emerged that the van driver got out of his van and physically assaulted people, using a weapon, between the crashes.
Ms Menzies had been with her one-year-old baby walking her daughter Ellie, eight, home from school. Both children are being treated in hospital for their injuries. She also has a disabled 10-year-old child, who is on a "dream holiday" in Disneyland, Florida and is unaware that she has died.
Detective Superintendent Hurley urged witnesses to get in touch, and asked for information about a black Renault Clio seen driving on the wrong side of the road of Western Avenue, not far from Cowbridge Road West, where one crash happened.
Police first received calls about an incident in Crossways Road in Ely at 3.30pm on Friday.
This was soon followed by other reports of collisions in several locations in the west of the city, including Grand Avenue, Cowbridge Road West and the Leckwith Retail Park.
There was no full registration for the Clio, but officers said it carried a 05 plate.
Floral tributes were laid at the scene, outside Ely fire station, where Ms Menzies died.
Among those paying their respects was local Labour MP Kevin Brennan.
He said: "It's absolutely shocking what has happened and the fact that someone has appeared to use a vehicle as a weapon.
"Karina was a well-liked mother who had three children. One of her children is disabled and is currently on a dream holiday in Florida.
"This incident is beyond senseless and has rocked the whole community."
Ely subpostmaster Shady Taha, 29, served two young girls and a woman moments before one of the crashes in Grand Avenue, immediately outside a row of shops.
He said: "All of a sudden I heard a bang. I looked out and across the road one girl was on the floor and the other girl was screaming.
"I heard a van speed off but I did not see it."
Other eyewitnesses said pedestrians were deliberately targeted by someone driving a white van.
A female shop worker, who did not want to be named, said: "We had a customer in our shop who said the van mounted the kerb like the driver wanted to run down young kids with their parents."
Superintendent Julian Williams said: "This is a tragic incident that has affected a large number of people, and we thank the people of Cardiff for their help and support.
"Incidents like this are extremely rare here, as they are across South Wales, and we want to reassure the public that a significant number of officers are working on the investigation, including a number of specialist resources."