Not a good idea to go hard at the start of a ride. In fact, it's an awful idea. In addition to road riding, I've been using the Schwinn 240 recumbent downstairs. I go for an hour at a time. My goal is to go at a hard enough pace so I have nothing left after the hour. However, the first few minutes are by necessity at a lower pace to let my body acclimate as my heart rate ramps up, the blood starts flowing, the lungs start working harder. My custom program starts at level 5 for the first 2 intervals (1.5 minutes per interval in a 1 hour ride), then bumps to 6, and finally 7. After that it's a mix of mostly 7 and 8, with the 8's usually followed by 5's or 6's for a little recovery. I also threw in 1 interval at 12 towards the end just to keep it interesting. Anyway, one time I made the mistake of trying to start at level 7 instead of 5. I only got 10 minutes in, then had to stop. The legs were cramping, nothing else felt right. Prior to this ride, I had worked up to 21 miles in an hour, with an average power of 175 watts. It took about 5 more rides before I was back at the level. Moral of the story here-even minor increases at the start of a ride can have serious consequences.
Now let's talk road riding. It's easy to be deluded into going fast at the start of a ride because you're fresh. Especially if I'm going for a long ride, I try not to fall into that trap. The start of my rides is usually the same route. Altitude drops about 20 feet roughly 1/2 mile after the start. After that it's an 80 foot altitude gain over the next 2.5 miles. I can usually do this "warmup" 3 mile segment in 12 minutes or less. I've done it in 10.5 minutes when I'm feeling great. On the flip side it's taken 13 minutes when I'm feeling lousy, or perhaps encounter headwinds. 11:15 seems to be about average if I'm riding regularly. If I went flat out, I could probably make it in under 10 minutes most of the time, but I would have nothing left for the remainder of the ride.
After that, my pace depends upon how far I plan to go. An hour ride, maybe I'll be at a power level where I'll hold 21-23 mph on level roads. Average speeds of course are less because hills and winds always work against you, and in NYC you can never ride at a continuous, steady pace for long before encountering traffic, potholes, red lights (which necessitate at least slowing down enough to see if you can safely pass), etc. Maybe for the portions of my ride where I'm on arterials then I'll average in the 17-18 mph area, although 20 mph isn't unheard of. On a longer ride, I drop the pace by 1 or 2 mph. May not seem like much, but the human body is a peculiar machine. Just cutting power output from, say, 175 watts, to 160 watts could increase endurance by 50%. And it doesn't affect average speed much, either. On some longer rides I've averaged overall a few ticks over 16 mph, although high 15's is more typical. I rarely average over 17 mph on shorter 1 hour or 45 minute rides.
I have done a few "ride a mile as fast as I can" spurts, but this was only maybe towards the end of a ride, after I had thoroughly warmed up. I forget my best time, although a few seconds under 2 minutes sounds about right. After the spurt, I still ride another few minutes to let my body recover. Never go straight to 100% and then back to zero. Worst thing for your body, and also your enjoyment.