Thank you very much for your help... for the most part it all makes sense, but I have a couple more questions if you don't mind about that problem.

1. After you helped me figure out what the heaviside function was, I looked it up on the internet, and

Heaviside Step Function -- from Wolfram MathWorld
declares it as 0 for x<0, 1/2 for x=0, and 1 for x>0. Do I need to put the x=0 part in there somehow???

2. How did you know how to substitute (v + 1/4) in for t?

3. Near the bottom, how did you eventually get rid of the integral?

Thank you for all your help, but if you wouldn't mind answering these questions too to help me understand, that would be amazing!