I want to buy an electric motorcycle but most of them are really slow. Is it possible to upgrade their battery or change their battery with car batteries after buying the motor?
You may be calling something by the name electric motorcycle that is not an electric motorcycle. Most production electric motorcycles are not considered really slow. A quality electric motorcycle will have substantial acceleration from a standing start. Today's electric motorcycles use high-tech Lithium chemistry based batteries which provide substantial power.
On the other hand, there are low-end electric scooters which would use old-tech lead-acid battery chemistry, which are low power compared to Lithium based batteries. Those models will have limitations with respect to mounting space on the frame and will not easily adapt to having the pack or battery changed to another type or size of battery.
If you were to purchase a low-cost, low-tech electric scooter that uses lead-acid batteries, you could replace the batteries with Lithium based batteries, but you would not be able to use the charger. Lead acid batteries have a different charge profile which would damage lithium batteries, or worse, create a situation resulting in a fire.
Additionally, lithium batteries are fairly expensive and would increase the overall expense of the low-cost scooter if your intent was to have the same range as the original battery system. It would also be challenging to safely install lithium cells in locations once occupied by lead-acid batteries.
I have a riding lawn mower that operates on lead-acid batteries, sealed lead acid valve regulated batteries, often called gel-cells. The batteries (quantity 20) do not last more than three years and cost me about US$600 to replace a few years ago.
I was able to locate a used lithium chemistry battery that once powered a Nissan Leaf. One module from the pack also cost US$600 and was a good replacement, except that it's going to be extremely challenging to fit this rather bulky module into the location formerly occupied by twenty tiny (relatively speaking). Even if I have to bolt it onto the back deck, in the open, it will be an improvement over the lead acid pack.
I expect this battery to last me five to ten years based on my previous experience with this chemistry and it also provides about three to five times the range (mowing duration) compared to the lead acid pack.
It can be done, but it's expensive and you would be better off to purchase a quality transportation device rather than rebuild a poor model.