Allah Almighty says: {That (is the Command); and whoever honors the symbols of Allah, then surely it is of the piety of the hearts.} [Al-Hajj: 32]
1) Honoring the symbols of Allah Almighty is done within the heart, speech, and actions.
2) Anything Allah ordained to be honored is of the symbols that must be honored, and this includes prayer.
704/1 - Abu Hurayrah (may Allah be pleased with him) reported that the Prophet (may Allah’s peace and blessings be upon him) said: “When the Iqāmah for prayer is announced, do not come to it running; come walking with tranquility. Pray what you catch up with and complete what you miss.” [Narrated by Al-Bukhāri and Muslim]
A version by Muslim has this addition: “For when anyone of you heads for prayer, he is in prayer.”
1) Prayer should be held in high regard, which includes coming to it in a polite, calm, and tranquil manner.
2) A person should join prayer in whatever position the Imam is in. He prays what he catches up with and completes what he misses.
Whoever catches up with part of the prayer with the Imam has gained part of the merit of congregational prayer, for the Prophet (may Allah’s peace and blessings be upon him) said: “Pray what you catch up with.” Hence, what some people do, as they remain standing until the Imam rises to the following Rak‘ah, is wrong.
705/2 - Ibn ‘Abbās (may Allah be pleased with him and his father) reported: “I accompanied the Prophet (may Allah’s peace and blessings be upon him) while we were returning from ‘Arafāt. He heard behind him a loud noise of beating and driving the camels forcibly. He pointed towards the people behind him with his whip and said: “O people, proceed calmly, for goodness is not attained by rushing.” [Narrated by Al-Bukhāri; partially narrated by Muslim]
-- --
1) We are instructed not to hasten on our way to places of worship, lest we lose calm and tranquility, and because it leads to crowdedness and pushing among people, which involves harm and disturbance.
2) Acts of worship are intended to be performed in the best manner, which includes calmness in performing and perfecting them.