It is narrated from Sayyiduna Usama bin Zaid (may Allah be pleased with him), who was riding with the Messenger of Allah (peace and blessings be upon him) when he set out from Arafat towards Muzdalifah: and the Messenger of Allah (peace and blessings be upon him) would make the camel go a little faster, and when he found an open space, he would make it go even faster.
Hadith Referenceسنن دارمي / من كتاب المناسك / 1918
Hadith Takhrijاس روایت کی سند صحیح اور حدیث متفق علیہ ہے۔ دیکھئے: [بخاري 1666] ، [مسلم 1286/283] ، [أبوداؤد 1923] ، [نسائي 3023] ، [ابن ماجه 3017، وغيرهم]
Brief Explanation
(Commentary on Hadith 1917)
From this it is understood that at the time of departing for Muzdalifah, one should walk briskly, but with consideration for those who are on foot, because the Messenger of Allah (sallallahu alayhi wa sallam) would only make his she-camel go fast when he found the path clear.