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What type of batteries do you want to use for the project; sealed lead acid, LiFePO4, or???

A 6000 Watt 72 Volt motor will pull 83.33 Amps when used at full power so it will require batteries that have a maximum discharge current rating higher than 83 Amps. I recommend using batteries with a maximum discharge current rating of 100 Amps to be on the safe side.

Batteries with that high of a discharge current are usually fairly large. I found specifications for our 12V 35Ah lead acid battery that states it will output 96 Amps for 5 minutes, and will output 33 Amps for 30 minutes. If the average battery drain is 33 Amps then 35Ah batteries will run the scooter for 30 minutes.

The wind resistance or drag to run a scooter at 45 mph is so high that my calculator says it will consume 5000 Watts to do so. I am not sure if this calculation is 100% correct though. However it will definitely consume a lot of power to cut through the air at that high of a speed. If the average power consumption is going to be 5000 Watts (70 Amps) then you might need 80Ah or larger batteries for a 30 minute ride time.

That is a lot of battery to put on a Vespa scooter. You might want to look into getting LiFePO4 batteries to help keep the weight down.

LiFePO4 stands for Lithium Iron Phosphate which is the mineral used for the cathodes of LiFePO4 batteries. LiFePO4 batteries are lightweight , able store a large amount of energy for their size, and have low toxicity when compared to most other types of batteries. Although LiFePO4 batteries are similarly priced to other types of Lithium-ion batteries they are around four times more expensive than lead acid batteries of the same capacity. However they have a three to four time longer lifespan which offsets the extra cost. One of the best advantage to LiFePO4 batteries over lead acid batteries is that they will not become damaged if they are not recharged for extended periods of time.