I once entered the house of Abū Ḥusayn with a group of Qurayshite women while the Prophet ﷺ was performing saʿy between al-Ṣafā and al-Marwah. She said, “He was moving so vigorously that his waist-wrapper kept swinging around, and he was telling his Companions, ‘Perform the saʿy, for Allah has prescribed saʿy for you.’”
Ahmad likewise reports: Suraij narrated to us; ʿAbd Allāh ibn al-Muʾammal narrated to us; ʿAṭāʾ ibn Abī Rabāḥ narrated to us from Ṣafiyyah bint Shaybah, from Ḥabībah bint Abī Tajrah, who said: “I saw the Prophet ﷺ making saʿy between al-Ṣafā and al-Marwah while the people were in front of him and he behind them. He was hastening until I could see his knees because of the intensity of his pace; his waist-wrapper was swinging about, and he was saying, ‘Perform the saʿy, for Allah has prescribed saʿy for you.’” Ahmad alone records this report.
Ahmad also transmits—from ʿAbd al-Razzaq, from Maʿmar, from Wāṣil, the freedman of Abū ʿUyaynah, from Mūsā ibn ʿUbaydah, from Ṣafiyyah bint Shaybah—that a woman told her she had heard the Prophet ﷺ between al-Ṣafā and al-Marwah say, “Saʿy has been prescribed for you, so perform saʿy.” That woman is Ḥabībah bint Abī Tajrah, explicitly named in the two previous chains.
A report from the maidservant of Shaybah ibn ʿUthmān states that she saw the Prophet ﷺ while he was making saʿy between al-Ṣafā and al-Marwah, and he was saying,
“Al-Abṭaḥ is not crossed except with vigor.”
Al-Nasāʾī recorded this ḥadīth. What is meant by saʿy here is simply moving from al-Ṣafā to al-Marwah and back again; it does not necessarily imply jogging or running. Allah has not made that level of speed obligatory. Thus, if a person were to walk calmly throughout the seven passages between the two points and did not jog in the low-lying area, it would still be valid according to the consensus of the scholars—indeed, we know of no disagreement on this point.