you are seriously the only person I have ever heard of who actually broke a bike ...like what were you doing. you do realize that you are supposed to pedal to propel yourself forward right?? that is all it is designed for.
I rode my old "Chicago Schwinn" all over when I was younger and didn't have a license yet... We moved out of district and my GF was 7 miles away, I used to wake up and eat 1/2 to 3/4 of a watermelon and then hop on the bike and go hang with her... I would sometimes make the trip 2 -3 times per day...
I got in such great shape that I could pedal up hill in 10th gear without downshifting.... I also liked to "lap" the die hard biker type guys in their spandex pants... I would be in my cut-off jean shorts and t-shirt and just up my pace until I caught up and passed them and keep going... They couldn't keep up with me...
I once had to race a storm front coming in... Every time I travelled north I would gain on the cloud front, then when I was going west, it would catch up to me... I just made it home about 5 minutes before the rain started and went to the end of my street at the top of the hill and cooled down with the wind blowing the storm in... That was exciting and fun to race a storm front and win...