Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) said: Fast riding was begun by the Bedouins. They would stand on both sides of the people, having hung up their staffs. When they departed, they hurried and rushed the people. And I saw the Messenger of Allah (peace and blessings be upon him), the neck of his she-camel touching the saddle, while he (peace and blessings be upon him) was saying: "O people, keep to tranquillity."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 9530
Sayyiduna Ibn Abbas (may Allah be pleased with them both) said that the Prophet (peace and blessings be upon him) departed from Arafah and reached Jam'; then he seated al-Fadl bin Abbas (may Allah be pleased with them both) behind him and said: "O people, righteousness does not lie in making camels and horses run, so keep to tranquillity."
I did not see that mount raising its forelegs until he (peace and blessings be upon him) reached Mina.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 9531
Sayyiduna Usamah bin Zayd (may Allah be pleased with him) said that he departed with the Messenger of Allah (peace and blessings be upon him) from Arafah, and his mount did not lift its feet high until he reached Muzdalifah. And Sayyiduna al-Fadl bin Abbas (may Allah be pleased with him) told me that he was riding behind the Prophet (peace and blessings be upon him) from Muzdalifah, and his mount did not lift its feet high until he had stoned the Jamrah.
In the narration of Affan: Sayyiduna Usamah bin Zayd (may Allah be pleased with him) narrated that he was riding behind the Messenger of Allah (peace and blessings be upon him) on the evening of Arafah, when he (peace and blessings be upon him) departed; and in the second hadith he says that Sayyiduna al-Fadl bin Abbas (may Allah be pleased with him) narrated it to him. [Sahih]
Tawus al-Yamani (may Allah have mercy on him) narrated something similar from the Prophet (peace and blessings be upon him), and he used to deny urging the mount on.
It is reported from Ata (may Allah have mercy on him) that these people invented the hastening, wanting to get ahead of the dust.
We have narrated urging the mount on in the valley of Muhassir from the Messenger of Allah (peace and blessings be upon him), and then from a large number of the Companions as well.
In such a matter, the correct view is the view of the one who affirms it, not the view of the one who denies it. And success is from Allah.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 9532