Below are several suggested projects for MA114.

The cycloid.
Assign problems 18-20 from section 8.5 of the text.  Students can
start to work on this during the first recitation of the semester. 

The Wallis product.  See the full description at
http://www.ms.uky.edu/~rbrown/courses/ma114cc
This can be assigned after the second exam.


The rainbow. 
This is described in Stewart's Calculus book, Calculus: Concepts and
context.

This can assigned immediately after the first test.