This Free Response Question includes the following concepts: Graphing Velocities of Carts during a Collision, Conservation of Linear Momentum, Conservation of Energy and Elastic Collisions.

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Link: AP Physics C 1998 Released Exam
The problem is on pages 153 - 155 of this pdf.
Their solution is on pages 173 - 175 of this pdf.
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Content Times:
0:37 Describing the Problem
1:38 Parts (a) & (a i)
2:18 Part (a ii) & (a iii)
3:12 Part (b)
5:49 Part (c i)
7:37 Part (c ii)
8:46 Part (d i)
10:14 Part (d ii)