This would all depend on what time of the day/night you are travelling, and when your are leaving your place of iqamah, which is the place of your residence or where you have intended to stay for ten days or more.
If you leave your place of iqamah after noon time, you must stay fasting. If you leave before noon, you must break your fast once you exceed the boundaries of the place of your iqamah.
As for the next day, if you arrive before noon, you are able to stay in the state of imsak, from Fajr time, until you reach your destination, and then adjust your intention and make it intention of wajib fasting.
If you arrive after noon, then you will not be able to fast for that day.
And Allah knows best.