Reaction of vinylacetylene (but-1-en-3-yne) with HCl Vinylacetylene contains both a double bond and a triple bond. We know that alkenes are more reactive to electrophillic addition reactions, so I thought that the $\ce{H+}$ from $\ce{HCl}$ would get abstracted via the double bond. 
However, the final answer says the product is 2-chloroprene, which is possible only if the triple bond abstracts it.

My teacher said that it was because of the carbocation stability and the abstraction of $\ce{H+}$ by triple bond forms a stabler carbocation and leads to conjugation and hence is favoured.

But then Wikipedia says that a 1,4 addition takes place and an allene rearrangement takes place.This means that the triple bond is the one that reacts first , but in a 1,4 fashion to form an allene which then rearranges. I was unable to find a mechanism for this allene rearrangement, why is this 1,4 addition favoured, and why it takes place. Also, what is the correct explanation: the first one or the second one?
Beyond a shadow of a doubt, the second explanation, involving an allene rearrangement is the correct one. As you said, alkenes are more reactive towards electrophilic addition and hence the addition of HCl happens first on the double bond to give 3-chloro-but-1-yne. What follows next is an intramolecular rearrangement, through a cyclic five-membered transition state, which is catalysed by CuCl with NH4Cl. It encompasses the abstraction of a hydrogen from the C4, the migration of the chloride from C3 to C2, following the formation of a double bond at C3 and C4. The product is referred to as chloroprene, which gives neoprene on polymerisation, a useful polymer. However the other explanation offered by your facilitator is used by many as a trick to remember the final product, (including, me!). Hope that helps!