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An eScooter-mounted mum was seen zooming towards Asda with her young child clinging on in front of her.
The incident was recounted to police at a council meeting in which the dangers of the motorised vehicles were raised.
Cllr Brian Sangha (Lab) told Gravesham council's crime and disorder scrutiny committee he had witnessed incidents around Gravesend town centre where people were recklessly driving eScooters.
These included the Asda incident in Overcliffe and another in Perry Street where two riders on one scooter hit a car door and fled into an alley on foot.
He said: "There is a risk to pedestrians in and around the town centre.
"These scooters are silent, very few of them have a horn or bell to warn people and they can travel of speeds of up to 15 mph."
Acting Inspector James Beautridge told councillors officers were using their resources to educate people about the use of eScooters after receiving a number of complaints.
He said the problem was "well on our radar" but was down to the lack of knowledge about how to legally use them on the roads.
eScooters are classified as Personal Light Electric Vehicles (PLEVs) so they are treated as motor vehicles; it is illegal to drive privately-owned eScooters on public roads including pavements and cycle lanes.
Hire schemes - such as one currently being rolled out in Canterbury on a trial basis aimed at students - work differently because they provide riders with third party insurance via an app, which also requires people to register their full or provisional driver's licence.
They can be ridden on private land with the permission of the landowner, and you should also wear a helmet.
Mr Beautridge added despite the fact he knew of incidents in the capital where people had died following incidents on eScooters, often those selling the vehicles don't communicate the laws to new riders and people often thought they were doing something good for the environment by making the purchase.
He said: "If I'm totally honest, it's something that's been overlooked for a long time.
"I think it's something that was in general low on the list of priorities, however, recently we have been receiving lots and lots of complaints from people of all ages, all areas, it's becoming an issue that needs to be addressed."
He said his team were talking to colleagues in the Met Police and in Canterbury, as well as committing one officer within the police's safety unit to tackle the issue.
Mr Beautridge said the approach his team was taking was to educate people and provide them with advice in the first instance of offending. Further stops could lead to a seizure order.
He said: "We don't want to criminalise the law-abiding member of the public who are actually ignorant to the fact they are illegal."
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