The Arabic word Qasr means shortening the prayers (Salah). There are several authentic narrations that the Messenger of Allah (ﷺ) would shorten his prayers whenever he (ﷺ) was on a journey. 
“And when you (Muslims) travel in the land, there is no sin on you if you shorten As-Salat if you fear that the disbelievers may put you in trial, verily, the disbelievers are ever unto you open enemies.” Qur’an Surah Nisa 4:101
Narrated Ya'la bin Umayyah: "I said to 'Umar [bin Al-Khattab]: 'Allah said: That you shorten the Salat if you fear and the people are safe (Quran 4:101).' So 'Umar said: 'I wondered about that just as you have wondered. So I mentioned that to the Messenger of Allah (ﷺ), and he said: "It is charity which Allah has given to you, so accept His charity." Book of The Traveller’s Prayers, Sahih Muslim 686, Sunan Abu Dawud Vol.2:1573 and Jami At Tirmidhi Hadith 3034
Hence, it is not made obligatory by Allah in Qur’an; rather it is an allowance (as Allah’s Messenger, PBUH, said in hadith above) from Allah, and refusing the charity or allowance from Allah will be an act of non-thankfulness on our part. Offering the obligatory (farz) prayers, either in normal circumstances and / or during a journey, is a Farz; the act of shortening the obligatory (farz) prayers during the journey is a Sunnah. 
Shortened prayers are permissible for a Muslim in any journey of 48 miles and above. If converted into kilometres, it works out to approximately 77 KMs. Ibn Umar (R), Ibn Abbas (R) used to shorten the Salat & stop fasting in a journey of four ‘Burud’ i.e. sixteen ‘Farsakh’ i.e. 48 miles (1 Farsakh equals 3 miles). So, whenever we travel for a distance of 48 miles (or 77 kilometres) and more, we can offer shortened prayer.
Detailed Rules of Law about the Prayer during Journey are mentioned in ahadith books. Narrated Ibn `Abbas(R): The Prophet (ﷺ) once stayed for nineteen days and prayed shortened prayers. So when we travel led (and stayed) for nineteen days, we used to shorten the prayer but if we traveled (and stayed) for a longer period we used to offer the full prayer. Book of Shortening the Prayers (At-Taqseer), Sahih al-Bukhari Vol.2:1080
Ibn Abbas(R) narrated: "The Messenger of Allah traveled on a journey and he prayed two Rak'ah for nineteen days." Ibn Abbas said: "So when we would stay somewhere for nineteen (days) we would pray two Rak'ah , and if we stayed longer than that we would complete the Salat." Jami` at-Tirmidhi 549
Narrated Abdullah ibn Abbas(R): The Messenger of Allah (ﷺ) had a stop of seventeen days in Mecca and he shortened the prayer (i.e. prayed two rak'ahs at each time of prayer). Ibn Abbas(R) said: He who stays seventeen days should shorten the prayer; and who stays more than that should offer complete prayer. Abu Dawud said: The other version transmitted by Ibn 'Abbas through a different chain adds: He (the Prophet) had a stop of nineteen days (in Mecca). Sunan Abi Dawud 1230 
Another factor which indicates that it is prescribed to omit the regular Sunnah prayers whilst travelling is the saheeh report from Ibn ‘Umar (may Allaah be pleased with him) who said: “The Prophet (ﷺ) combined Maghrib and ‘Isha prayer in Jam’ (i.e., Muzdalifah), reciting the iqaamah for each of them, and he did not pray Sunnah in between or after either of them.” Sahih al-Bukhaari, 1673
And it was narrated that Jaabir ibn ‘Abd-Allaah said: The Messenger of Allaah (ﷺ) traveled until he reached ‘Arafah, where he found that the tent had been set up for him in Namirah. He stayed there until the sun had passed its zenith, then he called for al-Qaswa’ (his camel) to be saddled, and he rode to the bottom of the valley, where he addressed the people. Then he told Bilaal to give the adhaan (call to prayer) then the iqaamah, then he prayed Zuhr, and then Bilaal recited another iqaamah and he prayed ‘Asr, and he did not pray anything in between.” Sahih Muslim, 1218 
Narrated Ibn Umar (RA): I accompanied Allah’s Messenger (PBUH) & he never offered more than two raka’at prayer during a journey. Abu Bakr (RA), Umar (RA) & Uthman (RA) used to do the same. Book of Shortening the Prayers (At-Taqseer), Sahih Al Bukhari 1102
Hadith mentioned above shows that Allah’s Messenger (ﷺ) always used to offer two raka’at for each prayer during a journey. However, at times he offered three raka’at also for Maghrib. Refer to following hadith:
Narrated `Abdullah bin `Umar(R): "I saw Allah's Messenger (ﷺ) delaying the Maghrib prayer till he offered it along with the `Isha' prayer whenever he was in a hurry during the journey." Salim narrated, "Ibn `Umar used to do the same whenever he was in a hurry during the journey." And Salim added, "Ibn `Umar used to pray the Maghrib and `Isha' prayers together in Al-Muzdalifa." Salim said, "Ibn `Umar delayed the Maghrib prayer because at that time he heard the news of the death of his wife Safiya bint Abi `Ubaid. I said to him, 'The prayer (is due).' He said, 'Go on.' Again I said, 'The prayer (is due).' He said, 'Go on,' till we covered two or three miles. Then he got down, prayed and said, 'I saw the Prophet (ﷺ) praying in this way, whenever he was in a hurry during the journey.' `Abdullah (bin `Umar) added, "Whenever the Prophet was in a hurry, he used to delay the Maghrib prayer and then offer three rak`at (of the Maghrib) and perform Taslim, and after waiting for a short while, Iqama used to be pronounced for the `Isha' prayer when he would offer two rak`at and perform Taslim. He would never offer any optional prayer till the middle of the night (when he used to pray the Tahajjud)." Book of Shortening the Prayers (At-Taqseer), Sahih al-Bukhari 1091, 1092 
And Allah knows best.
   http://www.quranandhadith.com/prayer-in-journey/