I'll start by just using a "carrito," without specifying what kind of "carrito" it is.
*** Talking about an object
Context. As we are speaking about an object, the word "carrito" would usually be interpreted as a shopping cart.
- "va en carrito," would definitely sound weird because given the indefiniteness one would expect to be talking about an animated being
- "va en el carrito," sounds natural, and could indicate two possible situations:
- to indicate where something should be located
— Dónde va (or dónde pongo) esta caja?
— Va en el carrito (no en la bolsa).
- to indicate where something is already located
— Dónde está la caja?
— Va (or está) en el carrito.
*** Talking about a being
Context. As we are speaking about a living being, the word "carrito" would now need to be interpreted as a stroller.
- "va en carrito," implies that the child is habitually carried around in the stroller
– por su edad, el niño va en carrito
Notice again how this would be a weird expression if "carrito" were to mean a shopping cart.
- "va en el carrito," would now be only used to indicate where is the child
— Dónde está el niño?
— Va (or está) en el carrito.
It would be a little strange to use this expression to indicate where should the child go, in which case one might use the verb "poner."
— Dónde pongo al niño?
— Ponlo en el carrito.
Once a noun is made specific by using an adjective, like in "de compras" in this case, the accompanying definite article is usually used, though one could also use the indefinite article to specify that we are talking about one non-specific noun.
- va en el carrito de compras
- va en un avión de pasajeros
The article may be omitted if one is talking about where something is transported (or not) in general terms.
– ese tipo de equipo va en tren de carga
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