Getting faster ...
Those new to cycling are sometimes enamored with getting faster ... to keep up with their newfound teammates. That makes a lot of sense. But how to get there without getting hurt?
One must get stronger in order to ride faster, particularly over longer distances. The best cure for getting stronger is riding as much as possible (not as long as possible). Cycling every day will do more for your stamina and strength than about anything else. The more you ride ... the more you can ride. You'll get faster and be able to go further.
Getting faster is somewhat a mental game too. The more you think about it the harder it is. Be aware that every day you go out on your bike, your body is not the same as yesterday or the day before. You'll have some days where you ride strong, others not so much. Mentally you start to wonder about those "bad days" ... and I say "don't let it bother you." It happens.
Another key to getting faster is to ride solo more than 50% of the time and DO NOT look at your speed. Concentrate on cadence and let your legs give you whatever they have for that day. Doing this many days in a row will provide surprising results -- you will get faster.
Now get out there and pedal!