首先简单的说一下arrive的用法
arrive为不及物动词,即：不能直接跟宾语,如果需要有宾语,得和at 或 in搭配使用.如：
Has he arrived?他到了吗?（没有宾语）
He arrived in Beijing yesterday.他昨天到北京的.
I arrived at the airport very early.我很早就到了机场.
至于arrive后面跟at和in的区别,可以这样记忆：
in 表示到达的地方比较大,如：国家、省、市、镇等
at表示较小的地方,如：村庄、市内的某个地方（机场、商店、广场等）
现在分析你的句子
1.the train always arrives on time.
在本句中,on time是短语,准时.是时间状语.而不是和arrive在一起连用的.
句子意思是：火车总是准时抵达.
2.the car always arrives on the farm 这个是错误的.不能用on
3.the car always arrives at the farm （arrive at 到达小地方）
不懂继续追问至于arrivein+大地方和arrive at +小地方我倒晓得但是我觉得 the car always arrives on the farm我的理解也还是有理的啊就是把说on the farm 当地点状语。况且楼下那位也说我说得对呐、呵呵， 我查了好几本词典～ 我给你列举麦克米伦Macmillan English Dictionary for Advanced Learners上的用法举例吧。我只是觉得从来没有见过用arrive on 表示地点，就是用也应该是非常罕见。 1. The verb arrive is never used with the preposition to: ✗ He meets them at an inn before they arrive to the house. ✓ He meets them at an inn before they arrive at the house. Arrive can be used with at or in: ▪you arrive at a building (such as an airport or restaurant)例句：…the scene in which Robyn arrives at the factory for the first time ▪you arrive in a geographical location (such as a city or country) 例句：A delegation of senior French ministers will arrive in London today.▪you can also use arrive at in a figurative way, meaning ‘to reach a particular goal or point in a process’ Quite independently, we all arrived at the same conclusion. The court will arrive at a final decision next week.Note that with the word home, no preposition is used: ✗ When they finally arrive at home, all they want to do is sleep. ✓ When they finally arrive home, all they want to do is sleep.在用法中并未涉及on.我觉得，你不要在纠结这个问题了，我们在学习语言，不是创造语言。只是用来和别人沟通罢了，你非要说可以，也许过很多年，很多人都在用arrive on了个人觉得还是不要用on·····希望帮到你