Question: If the time for Salat al-Asr begins when a group of men is performing Salat az-Zuhr in jama’at and if those who have not offered Salat az-Zuhr come, join the jama’at, and offer Salat az-Zuhr with them, will the salats of them be considered qada (offering a salat after its prescribed time) or ada (offering a salat within its specified time)?
ANSWER
The performance of those who joined the jama’at before the time for Salat az-Zuhr was over is considered ada. The performance of those who joined the jama’at after the time for it was over is considered qada. It is written in the book Endless Bliss:
“The person who makes his niyyat [intention] as “To perform today’s Salat az-Zuhr” will have made qada of the Salat az-Zuhr if its time has been over. If he thinks that the time is over and makes his niyyat as “To make qada of today’s Salat az-Zuhr,” he will have made ada of the Salat az-Zuhr when he finds out later that its time was not over.”

If the latecomers decide to follow the ijtihad of Imam-i A’zam, they will have performed Salat az-Zuhr at asr-i awwal. In this case, they must perform Salat al-Asr at asr-i thani.

Question: What is the least thing a person must do so that he may be considered to have caught the salat in time?
ANSWER
When performing Salat al-Fajr, one has to say the salam before the sun rises. As for the other four salats, they are considered to have been performed in time if the initial takbir is said before the end of the prescribed time in the madhhabs of Hanafi and Hanbali, and if one rak’at is completed in the madhhabs of Maliki and Shafi’i. In the Hanafi Madhhab, one has committed a minor sin if one does not complete all of the rak’ats of a salat within its time. (Radd-ul-mukhtar, Tahtawi, Al-Fiqh 'Ala Al-Madhahib Al-Arba'ah)

If the sun rises when one is performing Salat al-Fajr, one’s salat will not be valid. However, if the sun sets when one is performing Salat al-Asr, it will be valid.