Kinda depends on how much it is used for business vs commuting and general run of the mill personal use.

No one "deducts" the purchase of a car. They invested the funds into an Asset. They didn't Spend anything. The car is still right there. There are regulations for how it gets treated for tax filing purposes.

Are you familiar with the tax rules related to this person's business activities and the use of a personal vehicle with mixed personal and business trips?

The IRS has lots of resources:

https://www.irs.gov/businesses/small-businesses-self-employed/deducting-business-expenses