You could drive 1000 miles in one day but you would have to drive a lot without stopping.
And if you drove at 70 MPH constantly then it would take you roughly 16 to 17 hours to drive 1000 miles when factoring in stops for gasoline.
For one person to drive a vehicle 1000 miles in one day would be really hard and it would increase your chances of getting into a car crash.
Driving gets very tired and I have drove 800 miles before and it was very hard on me and now I only drive at most 500 miles which when factoring in rest stops and gasoline fill ups takes me around 11 hours.
Since there are only 24 hours in a day you need to only drive around 11 hours before stopping.
That is unless you have a second driver who can drive the additional 500 or so miles while you sleep.
But it's best to drive at most 500 miles and then rest for the day.
Even sometimes I will drive only 300 miles or even 250 miles in one day and then rest up for the rest of the day at a motel or even in my camper trailer that I sometimes pull.
Then I drive the other 250 miles and it makes it easier on me.