Yes you can.

But in a chapter 7, they will survive the bankruptcy.  In a chapter 13, you can discharge them (wipe them out).  

A chapter 7 will discharge most of your debts, but certain debts survive your chapter 7.  These are generally priority debts, such as most taxes, student loans, and child support/alimony.  Unfortunately, the bankruptcy code ( 523(a)(7) ) does not allow the discharge of:

“to the extent such debt is for a fine, penalty, or forfeiture payable to and for the benefit of a governmental unit….”

This means that after a chapter 7 bankruptcy, you will still owe those speeding tickets.

On the other hand, a chapter 13 will allow you to discharge those speeding tickets if you complete your court-confirmed plan.  In other words, those speeding tickets that can survive a chapter 7 will not survive your chapter 13.