Motorcar is a dated word, and not the main term used in any dialect of English.
Honestly I've never heard of it before, i doubt it is actually a word though(only word origin i can think of is "motorized carriage", apart from that theres only one type of car so a "motorcar" is redundant
Are you from the US? Because "motor car" is a perfectly acceptable word in UK English - just a little formal - you'd see it in a newspaper but it isn't generally used in everyday speech..
I've lived in both the UK and US, and will stick to what I wrote before— its usage is highly dated. These days, it's never used in the US, and only used in the UK by the older generation, albeit less and less commonly. For me, for example, it brings to mind images of Chitty-Chitty-Bang-Bang more so than anything else! Just my opinion :)
Here in NZ you will certainly hear it. Any news on the radio referring to accidents or congestion always use "motor car" not just "car" and a quick online search of the local press comes up with 162 instances of "motor car" and 346 of "motorcar" on just one site.