The SR71 has thermal expansion problems because it is in the atmosphere. In space, you no longer have such problems from friction in the atmosphere, but you have other problems to solve like dealing with solar radiation/darkness cycles (if you are in orbit).
If you watch the launch video (start at about 21:30), it has a little speed indicator in the upper right corner starting at T-4 seconds. The counter just steadily increases while the rockets are burning. When the rockets shut down, it stops accelerating or even slows down until the next rocket kicks in.
The rate at which the rocket accelerates is quite often about the rate at which a motorcycle or sportscar accelerates. On the speed indicator, 100km/h is about 60 mph, and often you will see between 2-4 seconds for the number to increase by 100. At one point it is accelerating much faster than that - when it is high, out of the atmosphere, but still being driven by the main booster, it's got a lot of power and no air to slow it down. Once it's in space, there's no hurry - the big hurry on launch is to get out of the atmosphere that steals energy through friction. This is why the second stage only has one engine - they can just burn it longer.
During the launch, you can see on the timeline (and hear announcements about) Max-Q - that's maximum dynamic pressure, right when it goes supersonic. The vehicle is going faster and faster, and higher and higher, and so at some point you get the maximum wind resistance. Higher than that, and the thinner air resists less. Lower than that, and you're going slow enough to have lower wind resistance.
Many rockets, including Falcon Heavy, do not operate at full throttle the entire time - it would be possible for you to exceed the structural strength of the rocket if you go too fast at too low an altitude. So, that's why you hear the announcers talking about throttling down and throttling up. They throttle down before Max-Q, then after it they throttle back up.
Does any of that help? If you have any questions about the launch I can try to answer them.