Conjugated Dienes and the Allylic Position (Kinetic vs Thermodynamic Control)

Problem # 1281

Allylic and benzylic halides tend to undergo both SN1 and SN2 substitution reactions at a faster rate than their alkyl counterparts.

For example, both allyl chloride and benzyl chloride undergo SN2 reaction at a faster rate than propyl chloride. 

The same holds true for SN1 reactions: a 2° allyl or benzyl halide undergoes SN1 reaction faster than a 2° alkyl halide. Explain.

Problem # 572
 

Let's work through a conjugate addition problem.

Write out the mechnanism for the formation of the 1,2 and 1,4 products of the reaction below.